A post-quantum privacy-preserving multimodal biometric authentication framework integrating ML-KEM (Kyber) and fully homomorphic encryption

1 Introduction

Secured authentication protocols are essential for ensuring security in modern digital infrastructures such as financial systems, healthcare platforms, and government services. Authentication enables secure access control and identity verification across digital platforms [1]. Traditional authentication approaches based on passwords or tokens remain vulnerable to well-known threats such as credential leakage, phishing attacks, replay attacks, and brute-force compromises [2–4]. To address these limitations, the introduction of biometric authentication has proven to be an effective substitute because it enables identity verification using inherent physiological attributes such as facial features, iris patterns, and fingerprints [5].

Although biometric authentication enhances usability and strengthens identity binding, it introduces severe security and privacy vulnerabilities in the system. Biometric templates stored in central databases are susceptible to template inversion, replay, and database compromise attacks [6, 7]. Moreover, unimodal biometric systems are vulnerable to spoofing attacks with synthetic biometric artifacts produced using modern machine learning algorithms, such as deepfake generation or adversarial manipulation [8].

Simultaneously, the development of large-scale quantum computing is a fundamental threat to the cryptographic primitives that underpin modern authentication infrastructure. RSA and Elliptic Curve Cryptography (ECC), which are types of public-key cryptography, are insecure when sufficiently powerful quantum computers exist because of Shor’s algorithm, which allows the efficient computation of integer factors and discrete logarithms [9]. Symmetric cryptographic primitives also suffer from diminished security margins under the Grover algorithm, which provides a quadratic speedup for brute-force key searches [10]. Therefore, there is a long-term quantum threat to authentication systems that rely on classical cryptographic schemes under the harvest-now-decrypt-later threat model.

Post-quantum cryptography (PQC) has become a critical research area with the objective of developing cryptographic primitives that are resistant to quantum-capable adversaries [11, 12]. Lattice-based cryptography is one of these techniques that has received specific focus because of its sound theoretical basis and efficiency [13]. ML-KEM (Kyber) is a lattice-based hardness optimization of key encapsulation and has been finalized by the National Institute of Standards and Technology (NIST) as FIPS 203 post-quantum key encapsulation [14]. The basic security assumptions are outlined in Section 3.

Simultaneously, securing the biometric templates used in authentication is necessary to prevent the release of sensitive biometric data during storage and computation. Fully Homomorphic Encryption (FHE) is a type of cryptography that makes it possible to compute encrypted data without access to or revealing the underlying plaintext [15]. The Cheon–Kim–Kim–Song (CKKS) homomorphic encryption scheme [16] allows approximate arithmetic operations on data with real-valued data, confirming its suitability and applicability for encrypted-domain biometric matching. A description of the scheme, along with its security assumptions, is provided in Section 3.

Despite significant progress, most existing biometric authentication systems address biometric security, post-quantum cryptography, and privacy preservation independently. Many biometric systems are still based on classical cryptographic primitives, whereas privacy-preserving biometric frameworks often lack standardized post-quantum key encapsulation mechanisms. Therefore, the integration of post-quantum cryptography with encrypted-domain multimodal biometric authentication remains to be explored.

Recent studies have partially investigated the individual components of this domain. Hybrid post-quantum cryptography (PQC)-based biometric encryption frameworks have been proposed for consumer systems [17], and decentralized quantum-secure biometric architectures have also been explored [18]. In addition, emerging studies have incorporated PQC into biometric spoof detection [19].

In our prior work [20], we introduced a post-quantum authenticated session protocol based on ML-KEM and ML-DSA for secure communication. Building on this foundation, the present study extends quantum-resistant security to privacy-preserving multimodal biometric authentication using fully homomorphic encryption.

In parallel, homomorphic encryption-based systems such as CryptoFace [21] and homomorphic encrypted biometric fusion approaches such as HEFT [22] enable encrypted-domain biometric matching. However, these approaches incur high computational overheads and do not incorporate standardized post-quantum key encapsulation mechanisms (e.g., ML-KEM).

Despite these advancements, the following limitations persist.

• Lack of post-quantum secure biometric frameworks: Most existing biometric authentication systems rely on classical cryptographic primitives such as RSA and ECC, rendering them vulnerable to quantum adversaries using Shor’s algorithm.
• Absence of encrypted-domain multimodal biometric matching: Although homomorphic encryption has been applied to biometric protection, prior studies have predominantly focused on single-modal systems or partial encryption schemes, with limited support for fully encrypted-domain multimodal biometric matching.
• Limited integration of standardized PQC mechanisms: Existing privacy-preserving biometric systems rarely incorporate standardized post-quantum key encapsulation mechanisms, such as ML-KEM, resulting in incomplete quantum-resistant designs.
• High computational overhead without optimization: Homomorphic encryption-based biometric systems often incur significant computational costs, with limited use of feature optimization techniques to improve their efficiency and scalability.
• Lack of unified end-to-end architecture: Current approaches address cryptographic security, biometric fusion, and privacy preservation independently without integrating these components into a cohesive authentication framework.

These limitations highlight the need for a unified framework that integrates post-quantum security, encrypted-domain biometric processing, and robust multimodal authentication to ensure resilience against spoofing attacks.

This study proposes a unified post-quantum, privacy-preserving, multimodal biometric authentication framework that integrates ML-KEM (Kyber-1024) for quantum-resistant session key establishment with CKKS-based fully homomorphic encryption for encrypted-domain biometric matching. A Genetic Algorithm (GA)-based feature selection mechanism is employed to reduce feature dimensionality and mitigate homomorphic computation overhead, while feature-level fusion enhances robustness across face, iris, and fingerprint modalities and improves resilience against deepfake and biometric spoofing attacks.

Unlike existing approaches, which typically consider post-quantum key exchange, homomorphic biometric protection, or multimodal fusion in isolation, the proposed framework jointly combines (i) standardized post-quantum key encapsulation, (ii) encrypted-domain similarity computation over real-valued multimodal biometric features, and (iii) GA-based feature optimization for efficient homomorphic evaluation.

Furthermore, the proposed system provides a complete end-to-end realization, including formal security analysis under the MLWE and RLWE assumptions, explicit protocol modeling, and large-scale experimental validation (up to 5,000 users) for evaluating the latency, robustness, and noise tolerance.

To the best of our knowledge, based on an extensive review of the academic literature and patent disclosures, no prior study has jointly integrated post-quantum security, fully encrypted domains, and multimodal biometric authentication within a unified framework.

The proposed framework is grounded in lattice-based cryptographic constructions derived from computational hardness assumptions in high-dimensional algebraic structures, which have been widely studied in quantum-resistant cryptographic models and computational physics. This theoretical foundation underpins the design and integration of our proposed system.

The main contributions of this study are as follows:

• Unified post-quantum secure biometric framework: We propose a unified end-to-end framework that integrates ML-KEM (Kyber-1024) with CKKS-based fully homomorphic encryption, enabling simultaneous quantum-resistant communication and privacy-preserving biometric authentication.
• Encrypted-domain multimodal biometric processing: A secure processing pipeline is designed to perform encrypted-domain biometric matching over fused multimodal features, ensuring that biometric templates remain protected during storage and computation.
• GA-based feature optimization for efficient homomorphic evaluation: A Genetic Algorithm (GA)-based feature selection mechanism is introduced to reduce feature dimensionality and significantly improve the computational efficiency of the homomorphic similarity evaluation.
• Accurate and scalable encrypted-domain similarity computation: A CKKS-based similarity computation mechanism is implemented to support real-valued biometric feature matching, enabling accurate and scalable authentication in an encrypted domain.
• Robust multimodal authentication against spoofing attacks: The multimodal fusion of the face, iris, and fingerprint modalities enhances the robustness against deepfake and presentation attacks, thereby improving the overall system resilience.
• Comprehensive implementation and evaluation: The proposed framework was validated through extensive experiments on public datasets, including scalability analysis (up to 5,000 users), cryptographic parameter specification, and performance evaluation in terms of latency, accuracy, and noise tolerance.
• Novel unified integration: To the best of our knowledge, and based on an extensive review of the academic literature and patent disclosures, existing approaches typically combine at most two of the following components: post-quantum cryptography, homomorphic encryption, and multimodal biometric authentication. However, no prior study has jointly integrated all three within a unified post-quantum, privacy-preserving authentication framework.

The remainder of this paper is organized as follows. Section 2 reviews the related work, and Section 3 introduces the mathematical preliminaries. Section 4 presents the formal system and protocol models, followed by the threat model in Section 5 and the formal security analysis in Section 6.

Section 7 describes the proposed architecture and methodology, and Section 8 details the implementation and experimental setup of the study. The experimental design and evaluation protocols are outlined in Section 9, and the performance results are presented in Section 10. Section 11 provides an ablation study, and Section 12 evaluates the practical security under real-world attack scenarios.

Finally, Sections 13–15 discuss the implications, reproducibility aspects, and conclusions of this study.

2 Related work

Biometric authentication systems have extensive application deployments in security-sensitive infrastructures; however, existing implementations face serious privacy and security challenges [23]. Moreover, the rapid development of quantum computing introduces novel threats to the classical cryptographic mechanisms deployed in authentication protocols [24]. A comprehensive overview of cryptographic techniques for biometric data protection is provided in [25], highlighting the limitations of current approaches under evolving threat models. These challenges have motivated the development of quantum-resistant authentication architectures.

This section reviews previous research studies in five areas: post-quantum authentication protocols, lattice-based cryptography, multimodal biometric authentication, homomorphic encryption for biometric protection, and decentralized authentication models. A summary of the representative studies is presented in Table 1. The comparison highlights that existing approaches predominantly address only subsets of the problem, typically combining at most two of the following components: post-quantum cryptography, homomorphic encryption-based biometric protection, and multimodal biometric authentication. A unified integration of all three components is absent in the current literature.

TABLE 1. Related work on post-quantum cryptography, multimodal biometric authentication, and homomorphic encryption.

2.1 Post-quantum authentication protocols

Post-quantum cryptography (PQC) involves the development of cryptographic mechanisms that remain secure against quantum adversaries [11, 12]. Quantum algorithms, such as Shor’s algorithm, break classical public-key cryptosystems, including RSA and ECC, by solving integer factorization and discrete logarithm problems in polynomial times [26]. Grover’s algorithm also accelerates brute-force key search for symmetric cryptographic primitives [27–29], hence the need for PQC.

Several PQC-based authentication protocols have been proposed to resolve this issue. [30] developed a Kyber-based authentication protocol for healthcare cloud environment. [31] proposed a three-party authentication and key exchange protocol based on the MLWE problem with formal security verification using BAN logic and the RoR model. [32] proposed a multi-factor authentication protocol for IoT systems using fuzzy commitment schemes; however, the absence of lattice-based PQC primitives limits its resistance to quantum attacks. Recent efforts have explored the integration of post-quantum cryptography into biometric systems. [33] proposed a hybrid HQC-AES-based fingerprint authentication framework, and [17] introduced a post-quantum hybrid encryption scheme for securing biometric data in consumer electronics. [18] further investigated a decentralized quantum-secure biometric authentication architecture.

In our prior work [20] proposed a post-quantum authenticated session protocol based on ML-KEM and ML-DSA, providing secure communication; however, it did not address biometric authentication or encrypted-domain processing.

2.2 Lattice-based cryptography for authentication

Lattice-based cryptography offers strong theoretical security and efficient implementation in post-quantum cryptographic systems [34]. NIST has standardized Kyber as FIPS 203 based on the Module Learning With Errors (MLWE) problem for post-quantum key encapsulation [14]. Other schemes, such as FrodoKEM, have powerful security guarantees but greater computational cost overheads [35].

Other post-quantum primitives include digital signature schemes such as Dilithium (ML-DSA) [14] and hash-based schemes such as [36]. Although these schemes provide quantum-resistant security, they are primarily designed for key exchange or signatures and do not directly address the issues of encrypted biometric template matching.

2.3 Multimodal biometric authentication

Multimodal biometric systems combine more than one biometric trait to enhance authentication accuracy and robustness compared to unimodal biometric systems [5]. By integrating multiple modalities, multimodal frameworks drastically minimize the spoofing risk and improve reliability under environmental variability [37].

Recent studies have explored multimodal biometric systems using deep learning techniques such as convolutional neural networks (CNNs) and generative adversarial networks [6]. Other frameworks combine multimodal biometrics with blockchain technology to enhance transparency and accountability [38]. However, many existing systems are dependent on classical cryptographic mechanisms, such as RSA and AES, which remain vulnerable to quantum attacks [39]. Recent studies have begun exploring the integration of post-quantum cryptography into biometric spoof detection, highlighting emerging threats such as presentation attacks in quantum-secure settings [19].

2.4 Homomorphic encryption for biometric protection

Homomorphic encryption enables biometric matching without revealing plaintext biometric templates [15, 40]. The CKKS scheme designed by [16] supports approximate arithmetic on real-valued vectors and is widely used in privacy-preserving machine learning and biometric processing.

Several studies have integrated homomorphic encryption into biometric authentication. Zuber and Sirdey presented an encrypted-domain k-nearest neighbor classification that can be used for biometric matching [41]. [42] suggested a hybrid biometric authentication method based on the Classic McEliece and FHE to protect the templates in terms of privacy. However, in real-time authentication settings, these systems are frequently characterized by high computational costs and low scalability rates owing to their heavy use of artificial memory and storage resources [43, 44]. In addition, their integration with standardized post-quantum key exchange mechanisms is limited. Recent studies have advanced the development of fully encrypted biometric inference systems. [21] proposed an end-to-end encrypted face recognition framework, and [22] demonstrated secure multimodal biometric fusion in an encrypted domain. Additional frameworks, such as CipherFace [45] and transciphering-based authentication [46] further improve encrypted inference capabilities. Similarity computation based on partially homomorphic encryption has also been discussed efficiently in [47]. However, standardized post-quantum key exchange mechanisms are not included in these approaches.

2.5 Decentralized authentication models

Recent studies have explored decentralized authentication frameworks that use blockchain technologies and zero-knowledge proofs. [48] proposed a post-quantum blockchain architecture for IoT authentication using lattice-based cryptography. Although the model ensures quantum-resistant communication security, it does not include biometric authentication. Similarly, [49] analyzed authentication vulnerabilities in cryptocurrency exchanges but did not incorporate post-quantum cryptographic solutions into their analysis.

2.6 Emerging threats in biometric systems

Recent studies have highlighted the emerging security risks associated with biometric authentication. [51] demonstrated that protected biometric templates may be vulnerable to reconstruction attacks from authentication outputs, raising serious concerns about information leakage. Furthermore, high-performance FHE-based systems such as [50] improve computational efficiency but remain limited to single-modality deployments, restricting their applicability to robust, real-world authentication scenarios.

2.7 Research gap

Despite extensive research on post-quantum cryptography, biometric authentication, and privacy-preserving computation, several critical limitations persist.

• Lack of integration between PQC and biometric authentication: Most biometric systems continue to rely on classical cryptographic primitives such as RSA or ECC, making them vulnerable to quantum attacks. Conversely, post-quantum authentication protocols rarely incorporate biometric modalities.
• Absence of encrypted-domain multimodal biometric matching: While homomorphic encryption has been applied to biometric protection, prior work primarily focuses on single-modal systems or limited evaluation scenarios. Fully encrypted multimodal biometric matching remains to be explored.
• Limited adoption of standardized PQC mechanisms: Existing privacy-preserving biometric frameworks often rely on non-standardized or theoretical cryptographic constructions, with minimal integration of standardized schemes such as ML-KEM (Kyber).
• Lack of unified end-to-end architecture: Current approaches typically address key exchange, biometric fusion, or template protection independently, rather than integrating them into a cohesive authentication pipeline.
• Absence of formally structured protocol design: Many existing systems describe high-level architectures without explicitly defining authentication protocols, message flows, or security composition, limiting their practical applicability.

These limitations highlight the need for a unified, efficient, and quantum-secure biometric authentication framework.

To address these challenges, this study proposes a post-quantum, privacy-preserving, multimodal biometric authentication framework that integrates ML-KEM (Kyber-1024) for secure key encapsulation, CKKS-based Fully Homomorphic Encryption for encrypted-domain biometric matching, and genetic algorithm-based feature selection for efficient multimodal fusion. By combining these components within a unified architecture, the proposed framework enables end-to-end secure and privacy-preserving biometric authentication.

3 Preliminaries

This section summarizes the core technical components and cryptographic primitives used in the proposed framework.

3.1 Multimodal representation

A multimodal biometric system integrates multiple biometric modalities to improve authentication accuracy and robustness. Let the biometric input set be defined as

B = B face , B iris , B fingerprint .

Feature extraction was performed independently for each modality as follows.

F i = f B i ,

where f ( ⋅ ) denotes the modality-specific feature extraction function.

The extracted features are then combined using a fusion function

F fused = Φ F face , F iris , F fingerprint ,

where Φ ( ⋅ ) represents a multimodal feature fusion operator.

Dimensionality reduction was performed using feature selection to improve the computational efficiency of encrypted-domain processing.

F selected = Ψ F fused ,

where Ψ ( ⋅ ) represents the feature selection function. In the proposed framework, genetic algorithm–based optimization is applied to identify the most informative feature subset. These selected feature vectors are subsequently encoded into CKKS plaintext slots before the encrypted similarity evaluation.

3.2 Kyber (ML-KEM)

Kyber is a lattice-based key encapsulation mechanism that is standardized by NIST FIPS 203. It enables the secure establishment of an ephemeral session key that is used to protect the transport of Fully Homomorphic Encryption (FHE) public artifacts within the authentication framework. Post-quantum key encapsulation mechanisms are essential for ensuring long-term security against quantum adversaries, particularly in biometric authentication systems, where sensitive data must remain secure over extended periods of time. Recent studies, such as [17, 18] have explored the integration of post-quantum cryptography into biometric security frameworks.

The key encapsulation and decapsulation processes are illustrated in Figure 1.

3.2.1 Mathematical security basis of ML-KEM

The security of Kyber is based on the hardness of the Module Learning With Errors (MLWE) problem. Given a uniformly random matrix

A ∈ Z q k × n ,

a secret vector s, and an error vector e, an MLWE instance is defined as

b = A s + e ( mod q ) .

The MLWE assumption states that recovering s from ( A , b ) or distinguishing ( A , b ) from uniform random samples is computationally infeasible for all polynomial-time algorithms.

Kyber achieves IND-CCA2 security via the Fujisaki–Okamoto transformation. Formally,

A d v ML - KEM I N D - C C A 2 A ≤ A d v MLWE B + negl λ ,

This implies that any adversary capable of breaking Kyber with a non-negligible advantage would imply an efficient solution to the MLWE problem.

Kyber-1024 corresponds to NIST security level 5, providing approximately 256-bit classical security and approximately 128-bit security against quantum adversaries under Grover-style search bounds.

3.3 Fully homomorphic encryption

Fully Homomorphic Encryption (FHE) enables computations to be performed directly on encrypted data without exposing the underlying plaintext values. In the proposed framework, the CKKS scheme is used because it supports approximate arithmetic on real-valued feature vectors, which is well suited for biometric similarity evaluation. Homomorphic encryption enables secure biometric matching without exposing sensitive templates, allowing similarity computations to be performed directly in the encrypted domain. This approach has been demonstrated in recent studies, such as [21, 22].

3.3.1 Core algorithms

The CKKS scheme consists of the following fundamental algorithms.

• Key generation:

p k , s k ← KeyGen

• Encryption:

c = Enc p k , m

• Homomorphic evaluation:

c * = Eval f , c 1 , … , c n

• Decryption:

m * = Dec s k , c *

These operations enable the encrypted-domain evaluation of similarity functions without revealing the underlying biometric template.

Real-valued biometric feature vectors were encoded using the CKKS approximate homomorphic encryption scheme prior to encrypted-domain similarity computation. The CKKS configuration employed a polynomial modulus degree of 8,192 with a coefficient modulus chain of {60,40,40,60}. Biometric feature vectors were packed into CKKS plaintext slots using SIMD-based vector encoding.

Prior to CKKS plaintext packing, real-valued biometric feature components were scaled by an encoding factor of Δ = 2 40 to transform approximate floating-point values into high-precision integer representations suitable for encrypted-domain arithmetic while preserving numerical stability throughout homomorphic computation.

Encrypted similarity computation was performed using element-wise squared difference operations, i.e., ( x − y ) 2, and the decoded slot values were aggregated across 45 feature slots to approximate encrypted Euclidean distance-based biometric matching.

3.3.2 Security assumptions

CKKS provides IND-CPA security under the Ring Learning With Errors (RLWE) assumptionas presented in Table 2. With the selected parameters

n = 8192 , coefficient modulus ≈ 218 bits ,

TABLE 2. Security level estimates for the cryptographic primitives used in the proposed framework.

Sources:NIST FIPS 203 [14–16].

The proposed scheme achieves an approximately 128-bit classical security.

Because CKKS does not provide IND-CCA2 security, Kyber-1024 was used to securely encapsulate and transport the FHE public and evaluation keys within the system architecture.

3.3.3 Key authenticity

Although Kyber provides confidentiality and forward secrecy for session key establishment, it does not provide endpoint authentication. Therefore, the proposed framework assumes an authenticated channel, such as a public key infrastructure (PKI) based on X.509 certificates combined with a post-quantum signature scheme (e.g., ML-DSA), or a TLS 1.3 deployment supporting PQC authentication.

3.4 Post-quantum cryptographic landscape

Quantum computing threatens several cryptographic schemes. Table 3 summarizes the effects of quantum algorithms on classical and post-quantum cryptographic systems.

TABLE 3. Quantum computing threats to cryptographic schemes.

4 Formal system and protocol model

This section formally defines the system entities, notations, authentication protocol, and security goals of the proposed post-quantum privacy-preserving multimodal biometric authentication framework.

4.1 System entities

The proposed system consists of the following components:

• Client ( C ): The user-side device responsible for biometric acquisition, feature extraction, and encryption of biometric data.
• Authentication Server ( S ): The central authority that performs encrypted-domain biometric matching and authentication decision-making.
• Biometric Database ( D B ): A secure storage system that maintains encrypted biometric templates.
• PQC Key Infrastructure ( K ): A cryptographic framework that supports key generation, distribution, and management using post-quantum primitives such as ML-KEM (Kyber).

4.2 Notation

Table 4 summarizes the mathematical, cryptographic, and protocol notations used throughout the proposed authentication framework.

TABLE 4. Mathematical and cryptographic notation used in the proposed framework.

The proposed framework employs the CKKS approximate homomorphic encryption scheme for privacy-preserving biometric matching. The polynomial modulus degree ( N ) determines the underlying polynomial ring dimension, while the coefficient modulus ( q ) governs the ciphertext noise budget and the supported multiplicative depth. Unlike exact homomorphic encryption schemes such as BFV and BGV, CKKS performs approximate arithmetic and therefore does not explicitly employ a plaintext modulus ( t ). Instead, numerical precision is maintained through the scaling factor ( Δ ). During homomorphic evaluation, ciphertext noise is controlled through rescaling, modulus switching, and relinearization to prevent excessive noise accumulation and ensure successful decryption throughout the authentication process.

4.3 Protocol definition

Let Π denote the proposed authentication protocol. The protocol consists of two phases: enrollment and authentication.

4.3.1 Enrollment Phase

• The client C captures biometric samples and extracts modality-specific features.
• Genetic Algorithm (GA)-based feature selection is applied to obtain a reduced feature vector T.
• The client encrypts the template:
• The client and server establish a session key using ML-KEM:
• The encrypted template c T and encapsulated key c are transmitted to the server S.
• The server stores c T in the biometric database D B.

4.3.2 Authentication phase

Otherwise, the authentication is rejected.

• The client C captures query biometrics and extracts feature vector Q.
• GA-based feature selection is applied to obtain the optimized query vector.
• The client encrypts the query:
• The encrypted query c Q is transmitted to the server S.
• The server retrieves the stored encrypted template c T and computes the encrypted squared Euclidean distance:
• The server decrypts the result:
• The server accepts authentication if:

d 2 ≤ τ 2

4.3.3 Protocol message flow (simplified)

• C → S : c , c T
• C → S : c Q
• S : d 2 ← D e c ( s k FHE , E v a l ( ( c Q − c T ) 2 ) )
• S → C : Accept / Reject

4.4 Security goals

Protocol Π is designed to satisfy the following security properties.

• Confidentiality of biometric templates: Biometric data remains encrypted during both storage and computation. No adversary can recover the plaintext biometric information without access to the secret key s k FHE.
• Authentication correctness: Legitimate users are authenticated with high probability, while unauthorized users are rejected based on the decision threshold τ.
• Forward secrecy: Session keys derived using ML-KEM (Kyber) are ephemeral and independent, ensuring that compromise of long-term keys does not reveal past session data.
• Post-quantum security: The protocol achieves security against quantum-capable adversaries under standard lattice-based hardness assumptions. In particular, the confidentiality of session keys relies on the MLWE assumption underlying the ML-KEM (Kyber), whereas the privacy of biometric data relies on the RLWE assumption underlying CKKS, ensuring resistance to both classical and quantum cryptanalysis.
• Resistance to replay attacks: Authentication sessions rely on fresh biometric inputs and session-specific cryptographic operations, preventing reuse of previously captured data.

4.5 Computational, memory, and communication complexity

The computational, memory, and communication complexities of the proposed authentication protocol are analyzed using asymptotic Big-O notation. Let n denote the dimensionality of the biometric feature vector after GA-based feature selection, and let N u denote the number of enrolled users.

4.5.1 Computational complexity

The computational complexity of each stage of the proposed authentication framework is summarized in Table 5.

TABLE 5. Asymptotic complexity of the proposed authentication framework.

The dominant computational cost arises from the Genetic Algorithm optimization during feature selection and the CKKS homomorphic operations performed during encrypted-domain biometric matching. Once the optimized feature subset has been generated, the online authentication stage is dominated by CKKS ciphertext multiplication, rotation, and slot summation operations, resulting in an overall authentication complexity of O ( n ⁡ log ⁡ n ) per query.

4.5.2 Memory complexity

The memory complexity is primarily determined by the storage of encrypted biometric feature vectors and intermediate ciphertexts generated during homomorphic evaluation. For each authentication query, the client stores one encrypted query vector while the server maintains one encrypted template per enrolled user. Consequently, the memory requirement per authentication session is O ( n ), whereas the total server-side storage complexity is O ( N u n ). The incorporation of GA-based feature selection reduces the feature dimensionality prior to encryption, thereby lowering ciphertext size, memory consumption, and encrypted-domain processing overhead.

4.5.3 Communication complexity

The communication cost per authentication session consists of the transmission of the ML-KEM (Kyber) ciphertext and the CKKS-encrypted biometric feature vector. The Kyber ciphertext contributes a constant communication cost of O ( 1 ) (approximately 1.5 KB), while the CKKS ciphertext scales linearly with the feature dimension due to SIMD-packed encrypted vectors, resulting in O ( n ) communication complexity (approximately 16–32 KB). Therefore, the overall communication complexity of the proposed protocol is

O 1 + O n = O n .

4.5.4 Scalability considerations

The proposed framework exploits SIMD batching in the CKKS scheme, enabling multiple biometric feature components to be processed simultaneously within a single ciphertext. This substantially amortizes the computational overhead associated with homomorphic evaluation and allows efficient large-scale biometric authentication. Consequently, although the theoretical complexity remains O ( n ⁡ log ⁡ n ), the practical execution time increases sublinearly with the number of encrypted feature comparisons due to parallel slot evaluation.

5 Threat model

This section defines the adversarial assumptions and security threats considered in the proposed post-quantum biometric authentication framework. Recent studies have shown that biometric systems may be susceptible to reconstruction attacks even when protected [51], motivating the need for encrypted-domain processing, as adopted in the proposed framework in this study.

We assume a powerful adaptive adversary operating under the Dolev–Yao model, which is capable of intercepting, modifying, replaying, and injecting messages across the communication channel. The adversary may also attempt biometric spoofing or adversarial machine learning attacks against the biometric recognition pipeline.

Specifically, the adversary is assumed to have the following capabilities:

• Generation of synthetic biometric samples (e.g., GAN-based face images or morphing attacks).
• Injection of adversarial perturbations into biometric inputs.
• Replay of previously captured biometric templates.
• Full network control enabling message interception, replay, and modification.

However, the adversary does not possess server-side secret keys, including the Kyber private and FHE secret keys. The adversary can observe all public parameters and perform adaptive query-based probing attacks on the authentication interface of the smart meter.

This study assumes an honest-but-curious trusted server model for encrypted-domain biometric computation and cryptographic key management. Consequently, actively malicious server-side behavior, including threshold manipulation, adversarial query orchestration, ciphertext replay strategies, or unauthorized logging of decrypted similarity scores, is considered outside the scope of the current implementation. Although CKKS-based homomorphic encryption preserves biometric confidentiality during encrypted computation, practical deployment environments may still introduce additional operational risks if the underlying server infrastructure becomes compromised [15, 16, 57, 58]. Addressing fully malicious or compromised server environments would require stronger adversarial protections, such as secure multi-party computation (MPC), trusted execution environments (TEEs), federated trust architectures, or distributed verification mechanisms [18, 59, 60], which remain important directions for future research.

The structured threat analysis and mitigation strategies are summarized in Table 6.

TABLE 6. Threat model for post-quantum secure biometric authentication.

We assume that the adversary may obtain the contents of the biometric database but cannot compromise the server-side secret keys or the trusted execution environment used for the cryptographic operations. Furthermore, an adversary may possess scalable fault-tolerant quantum computing capabilities that can execute Shor and Grover-type algorithms. Under these assumptions, the proposed framework aims to provide quantum-resistant communication security and privacy-preserving biometric authentication capabilities.

6 Formal security analysis

This section presents a formal analysis of the security properties of the proposed authentication protocol Π, based on the standard hardness assumptions underlying the cryptographic primitives employed in the system. The analysis was conducted using the adversarial model defined in Section 5.

6.1 Security assumptions

The security of the proposed framework relies on the MLWE and RLWE assumptions underlying the ML-KEM (Kyber) and CKKS, respectively, as described in Section 3.

• MLWE Assumption: Hardness of the Module Learning With Errors problem (Section 3).
• RLWE Assumption: Hardness of the Ring Learning With Errors problem (Section 3).

6.2 Game-based authentication security model

We define a standard game-based experiment between a challenger C and an adversary A interacting with protocol Π.

6.2.1 Setup

The challenger initializes system parameters and generates keys for ML-KEM and CKKS, providing public parameters to A.

6.2.2 Query phase

The adversary is allowed to make adaptive authentication queries, including biometric query submissions and protocol interactions.

6.2.3 Challenge phase

The adversary outputs a forgery attempt by submitting a biometric query intended to be accepted without corresponding legitimate enrollment data.

6.2.4 Winning condition

The adversary wins if the system accepts the forged authentication with non-negligible probability.

The authentication advantage of A is defined as the probability of winning this experiment beyond random guessing. This experiment captures authentication security under adaptive adversarial interactions in the presence of encrypted domain computation.

6.3 Adversarial advantage bound and security composition

To provide a unified view of the protocol security, we bound the overall adversarial advantage by combining the guarantees of the underlying cryptographic primitives and biometric decision processes.

Let A be a probabilistic polynomial-time adversary interacting with protocol Π. The authentication advantage of A is defined asThis bound is an informal composition argument rather than a tight reduction and is intended to provide an intuitive understanding of how the security of a system depends on its underlying components.

A d v Π auth A = Pr AuthSuccess Π A − Pr AuthSuccess Π rand .

The overall advantage can be upper bounded as

A d v Π auth A ≤ A d v MLWE B 1 + A d v RLWE B 2 + ϵ bio ,

where:

• A d v MLWE ( B 1 ) corresponds to breaking the ML-KEM (Kyber) security under the MLWE assumption,
• A d v RLWE ( B 2 ) corresponds to breaking CKKS encryption under the RLWE assumption,
• ϵ bio captures the intrinsic biometric error (FAR/FRR).

This bound is an informal (non-tight) composition argument intended to provide an intuitive understanding of how the overall system security depends on its underlying components, rather than a strict reduction-based proof.

6.4 Composition argument

The protocol comprises two independent components.

• ML-KEM (Kyber) for secure session key establishment (IND-CCA2 secure),
• CKKS for encrypted-domain biometric computation (IND-CPA secure).

These primitives operate on distinct layers, namely, communication security and confidentiality. Their composition preserves security under standard composition principles, assuming that the two components operate independently and no unintended information leakage occurs across layers, assuming no cross-layer information leakage.

The biometric decision process operates only on decrypted scalar outputs, ensuring that no intermediate encrypted information is exposed.

Therefore, the protocol achieves end-to-end security as long as the underlying MLWE and RLWE assumptions hold and the biometric error remains bounded.

6.5 Theorem 1: session key security

6.5.1 Theorem 1

Under the MLWE assumption, the session keys derived using the ML-KEM (Kyber) in protocol Π are indistinguishable from random keys to any probabilistic polynomial-time (PPT) adversary.

6.5.2 Proof sketch

ML-KEM (Kyber) provides IND-CCA2 security under the MLWE assumption (Section 3). Therefore, any adversary that distinguishes the derived session key K from a uniformly random value with a negligible advantage can be used to construct an algorithm that solves the MLWE problem with a non-negligable probability. Because the MLWE is assumed to be computationally difficult, such an adversary cannot be created. Hence, the session keys are computationally indistinguishable from the random keys.

6.6 Theorem 2: biometric template privacy

6.6.1 Theorem 2

Under the RLWE assumption, the encrypted biometric templates and query vectors processed using the CKKS scheme are computationally indistinguishable from random and reveal no useful information regarding the underlying plaintext biometric data.

6.6.2 Proof sketch

The CKKS scheme provides IND-CPA security under the RLWE assumption (Section 3). Therefore, the ciphertexts c T and c Q are computationally indistinguishable from the encryption of the random values. Any adversary capable of extracting information about the underlying biometric vectors from these ciphertexts can solve the RLWE problem. Because RLWE is assumed to be computationally difficult, biometric templates remain private during both storage and computation processes.

6.7 Theorem 3: end-to-end security of protocol Pi

6.7.1 Theorem 3

The protocol Π achieves end-to-end confidentiality and secure authentication under the combined security guarantees of ML-KEM (Kyber) and CKKS, assuming the hardness of the MLWE and RLWE problems.

6.7.2 Proof sketch

The protocol Π comprises two secure primitives: ML-KEM for session key establishment and CKKS for encrypted-domain biometric processing.

• From Theorem 1, session keys established using ML-KEM are indistinguishable from random and provide secure communication channels.
• From Theorem 2, biometric templates remain encrypted and private under CKKS during both storage and computation.

Because ML-KEM and CKKS operate independently on different components (communication security and data confidentiality), their composition preserves the security under standard composition principles. Therefore, the protocol ensures that no adversary can recover session keys or biometric data or manipulate authentication decisions without detection, except with a negligible probability of success.

Hence, protocol Π achieves end-to-end confidentiality and secure authentication under these assumptions.

6.8 Security against the threat model

We now map the formal security guarantees of protocol Π to the threat model defined in Section 5.

• Brute-Force Attacks: Mitigated by the high security level of ML-KEM (Kyber-1024), which provides strong resistance against exhaustive key search under both classical and quantum adversarial models.
• Database Compromise: Mitigated by storing biometric templates in encrypted form under CKKS. Even if the database is compromised, adversaries cannot recover the plaintext biometric data without access to the secret key s k FHE.
• Replay Attacks: Prevented through the use of fresh biometric inputs and session-specific cryptographic operations, ensuring that previously captured data cannot be reused.
• Man-in-the-Middle (MitM) Attacks: Mitigated by IND-CCA2 secure session key establishment using ML-KEM combined with authenticated communication channels (e.g., PQC-enabled TLS or ML-DSA-based PKI).
• Template Inversion Attacks: Prevented as biometric templates remain encrypted under CKKS during storage and computation.
• Adversarial AI/Deepfake Attacks: Reduced through multimodal biometric fusion, which increases robustness against spoofing attempts.
• Quantum Cryptanalysis: Mitigated through the use of lattice-based cryptographic primitives (MLWE and RLWE), which are believed to be resistant to quantum attacks.
• Side-Channel Attacks: Mitigated through implementation-level protections such as constant-time execution, masking, and hardened memory access patterns. Additionally, encrypted domain processing reduces the exposure of sensitive biometric data during computation.

6.9 Limitations of formal analysis

The presented formal analysis provides a proof sketch based on standard cryptographic assumptions (MLWE and RLWE) and does not constitute a full simulation-based or universally composable (UC) security proof. In particular, the interaction between biometric decision thresholds and cryptographic guarantees is analyzed at a high level rather than through a fully formalized security game. Extending the analysis to a complete UC framework or game-based proof remains an important area for future research.

6.10 Consistency between formal model and threat model

The formal security guarantees established in Theorems one to three align with the adversarial capabilities defined in Section 5. Specifically, the Dolev–Yao adversary model assumes full control over communication channels but does not access the secret keys. Under this model:

• IND-CCA2 security of ML-KEM ensures that intercepted ciphertexts do not reveal session keys, even under adaptive chosen-ciphertext attacks.
• IND-CPA security of CKKS ensures that encrypted biometric templates and queries remain indistinguishable from random ciphertexts, preventing template leakage under database compromise.
• The composition of these primitives guarantees that both communication security and data confidentiality are preserved under the combined adversarial model.

Thus, the formal analysis directly supports security claims under defined threat assumptions.

7 Proposed architecture and methodology

The proposed multimodal biometric authentication architecture, illustrated in Figure 2, integrates Genetic Algorithm (GA)–based feature selection, Kyber (ML-KEM) for post-quantum key encapsulation, Fully Homomorphic Encryption (FHE), and encrypted-domain biometric matching. The design ensures that biometric templates remain encrypted throughout their life cycle, including both storage and similarity computations. The system directly implements the formal authentication protocol Π defined in Section 4, where the enrollment and authentication procedures correspond to the respective protocol phases.

7.1 System workflow

The overall processing pipeline is shown in Figure 3. The authentication pipeline follows the structure of protocol Π and consists of the following stages.

• Biometric Acquisition: Face, iris, and fingerprint samples were obtained from publicly available PolyU benchmark biometric datasets for multimodal authentication experiments.
• Feature Extraction: Modality-specific biometric representations were generated from face, iris, and fingerprint samples using established biometric feature extraction techniques, including texture-based and structural descriptor methods implemented using Python image-processing libraries such as OpenCV (cv2), scikit-image, and NumPy. Face representations were derived using local texture encoding approaches, iris features were generated using frequency and texture based filtering methods, and fingerprint representations incorporated structural ridge and orientation characteristics for multimodal biometric processing.
• Feature-Level Fusion: The independently extracted modality-specific biometric representations were concatenated to form a unified multimodal feature vector comprising 95 initial biometric attributes.
• GA-Based Feature Optimization: A wrapper-based Genetic Algorithm (GA) feature selection mechanism was applied to identify the most discriminative multimodal biometric feature subset while reducing redundant feature dimensions associated with encrypted-domain biometric evaluation. Each GA individual was represented as a binary feature-selection vector, where selected bits corresponded to retained biometric attributes within the fused multimodal representation. Fitness evaluation was performed using the mean cross-validation accuracy obtained from a Random Forest classifier applied to the selected feature subset. The GA implementation employed tournament selection, two-point crossover, and bit-flip mutation operations across iterative generations to identify near-optimal multimodal feature subsets. The optimization process reduced the fused multimodal representation from 95 initial features to a final 45-dimensional biometric template.
• Post-Quantum Key Establishment: Kyber-1024 encapsulates a session key used to securely transport FHE public artifacts.
• Encrypted-Domain Matching: Biometric templates and query vectors are encrypted under CKKS and matched using homomorphic similarity computation.

7.2 GA-based feature selection and fusion

Biometric feature vectors corresponding to face, iris, and fingerprint modalities were derived from publicly available benchmark datasets and subsequently processed within the proposed multimodal authentication framework. The primary focus of this study is the integration of post-quantum cryptographic protection, encrypted-domain biometric matching, multimodal fusion, and GA-based feature optimization rather than the development of new biometric feature-extraction architectures.

The Genetic Algorithm (GA) is employed to identify the most discriminative subset of biometric features prior to encryption (see Figure 4). The GA iteratively optimizes feature selection through initialization, selection, crossover, mutation, and fitness evaluation.

The configuration of the Genetic Algorithm employed for multimodal feature selection is summarized in Table 7. The configuration parameters were selected to provide an effective balance between exploration and exploitation during the evolutionary search while maintaining computational efficiency and feature subset diversity for encrypted-domain biometric processing.

TABLE 7. Configuration parameters of the genetic algorithm used for multimodal feature selection.

The selected configuration was used consistently throughout all experiments to ensure reproducibility and stable convergence of the evolutionary optimization process.

The GA-based feature selection process employed a classifier-based wrapper optimization strategy in which candidate feature subsets were evaluated using the cross-validated classification accuracy of a Random Forest classifier. The fitness function, denoted by f ( ⋅ ), maximized the mean cross-validation accuracy of the selected feature subset. Feature dimensionality was progressively reduced through the evolutionary optimization process by iteratively eliminating non-discriminative features while preserving the most informative biometric characteristics, thereby improving computational efficiency without compromising authentication performance.

Before multimodal feature fusion, each biometric modality (face, iris, and fingerprint) was normalized independently using z-score standardization implemented via the StandardScaler function from the Scikit-learn library. This preprocessing operation transformed each feature distribution to zero mean and unit variance, ensuring that modality-specific feature ranges remained comparable prior to feature concatenation and GA-based feature selection.

The resulting feature subsets were fused across modalities to produce a unified multimodal representation. This fused vector integrates complementary information from the face, iris, and fingerprint modalities, improving robustness against spoofing and reducing feature dimensionality before encrypted-domain processing.

From a statistical perspective, multimodal fusion reduces the probability of false acceptance. Under the simplifying assumption of statistical independence between modalities, the fused false acceptance rate can be approximated as

F A R fusion ≈ ∏ i = 1 m F A R i ,

where F A R i denotes the false acceptance rate of modality i. This multiplicative reduction aligns with the observed improvements in the Spoof Acceptance Rate (SAR) and Equal Error Rate (EER) reported in the experimental evaluation.

7.3 Enrollment and authentication

7.3.1 Enrollment

During enrollment, multimodal biometric samples (face, iris, and fingerprint images) were captured and preprocessed. Feature vectors extracted from each modality undergo GA-based feature selection and feature-level fusion to produce a compact multimodal template for the target.

The fused template is encrypted using the CKKS homomorphic encryption scheme before it is stored. Kyber-1024 encapsulates a session key used to securely transmit the FHE public key, evaluation keys, and encryption parameters. The FHE secret key remains stored on the authentication server and is never transmitted to users.

7.3.2 Authentication

During authentication, users submit a new multimodal biometric query. The extracted and GA-optimized feature vectors were encrypted using the CKKS Scheme. The authentication server retrieves the corresponding encrypted template from the database and performs homomorphic similarity computation in the encrypted domain.

Only the final scalar similarity score is decrypted for the threshold comparison, ensuring that no intermediate biometric representation or raw template is exposed during the computation.

Algorithm 1: Enrollment Phase.

• Capture multimodal biometric samples
• Extract modality-specific feature vectors
• Apply GA-based feature selection to obtain F selected.
• Fuse selected features into a unified template vector T.
• Encrypt the template using CKKS
• Establish a session key using ML-KEM (Kyber)
• Use session key K to securely transmit the CKKS public key, relinearization keys, and Galois keys.
• Store the encrypted template c T in the biometric database.

Algorithm 2: Authentication Phase.

• Capture query biometrics and extract feature vector Q.
• Apply GA-based feature selection and feature fusion.
• Encrypt the query vector
• Retrieve the encrypted template c T.
• Compute the encrypted squared Euclidean distance
• Decrypt the similarity score
• Accept authentication if d 2 ≤ τ 2; otherwise, reject.

7.4 Homomorphic computation of biometric matching

The CKKS scheme was selected instead of integer-based homomorphic encryption schemes, such as BFV, because biometric feature vectors are inherently represented as real-valued data. CKKS supports approximate arithmetic on floating-point values, making it well suited for encrypted-domain biometric similarity computations.

Let

c Q ← E n c p k FHE , Q , c T ← E n c p k FHE , T

denotes the ciphertexts that SIMD-pack the biometric feature vectors.

Implementation notes:

• After each ciphertext–ciphertext multiplication, relinearization and rescaling operations are applied to control ciphertext noise growth.
• Ciphertext rotations require corresponding Galois keys for slot-wise operations.
• Squared Euclidean distance is used instead of Euclidean distance to avoid costly square-root computations in the encrypted domain.

7.5 Encrypted squared Euclidean distance

Squared Euclidean distance is employed as the similarity metric due to its compatibility with homomorphic operations and low multiplicative depth requirements.

c Δ ← E v a l c Q − c T

c d 2 0 ← E v a l c Δ ⊙ c Δ

Slot-wise summation is performed using rotation-and-add operations as follows:

c d 2 ← E v a l ∑ k ∈ R R o t k c d 2 0

After decryption:

d 2 = D e c s k FHE , c d 2 ≈ ∑ i = 1 n Q i − T i 2

7.5.1 Decision rule

The authentication threshold τ is determined using Receiver Operating Characteristic (ROC) analysis on a validation dataset. The selected operating point corresponds to an Equal Error Rate (EER) of 0.2%.

Authentication is accepted if

d 2 ≤ τ 2

7.6 Kyber key encapsulation process

ML-KEM (Kyber-1024, FIPS 203) is used to derive a fresh session key for protecting the transmission of FHE public artifacts.

p k K , s k K ← K y b e r . K e y G e n

c , K ← K y b e r . E n c a p s p k K

K ′ ← K y b e r . D e c a p s s k K , c

The derived session key K is used to protect the transmission of

P K FHE , E v a l K e y s , p a r a m s FHE

The FHE secret key s k FHE remains securely stored on the authentication server and is never transmitted to users. The respective roles of ML-KEM (Kyber-1024) and CKKS in the proposed authentication framework are summarized in Table 8.

TABLE 8. Cryptographic roles in the proposed architecture.

7.7 ISO/IEC 24745 compliance mapping

• Irreversibility: Biometric templates remain encrypted under CKKS during storage and computation.
• Unlinkability: Session-specific encryption contexts prevent cross-database correlation.
• Renewability: Templates can be re-encrypted under new FHE keys if compromise is suspected.

7.8 Design choices

7.8.1 Choice of CKKS over BFV

The CKKS scheme was selected because it supports approximate arithmetic on real-valued feature vectors that are commonly produced in biometric systems. In contrast, integer-based schemes, such as BFV, require additional encoding overhead and are less efficient for floating-point operations, making CKKS more suitable for encrypted-domain biometric matching than BFV.

7.8.2 Choice of ML-KEM (Kyber)

ML-KEM (Kyber) is chosen due to its standardization (NIST FIPS 203), strong security guarantees based on the MLWE problem, and practical efficiency. Compared with alternative post-quantum schemes such as FrodoKEM, Kyber provides a favorable balance between computational performance and security.

7.8.3 Choice of squared Euclidean distance

Squared Euclidean distance is used as the similarity metric because it requires only addition and multiplication operations, making it well-suited for homomorphic evaluation. This avoids computationally expensive operations, such as square root computation, and reduces the ciphertext noise growth.

8 Implementation and experimental setup

The proposed authentication framework was evaluated in a simulation-based environment under controlled conditions rather than in a live-deployment scenario. All cryptographic operations, biometric feature processing, and encrypted-domain computations were performed on a local system.

A summary of the primary implementation and evaluation settings is presented in Table 9. Additional implementation details, cryptosystem configurations, workload parameters, reproducibility settings, and hardware/software environment specifications are provided in the accompanying Supplementary Material.

TABLE 9. Methods transparency: cryptosystem, biometric workload, and implementation environment settings used during evaluation.

8.1 Software environment and cryptographic libraries

The implementation was developed using C++ and Python to separate the cryptographic operations from the biometric preprocessing tasks.

• Fully Homomorphic Encryption: Microsoft SEAL version 4.0 implementing the CKKS approximate homomorphic encryption scheme.
• Post-Quantum Cryptography: Kyber-1024 (ML-KEM, FIPS 203) reference implementation from the PQClean repository.
• Programming Languages: C++ for cryptographic operations and homomorphic evaluation; Python for biometric preprocessing and GA-based feature selection.
• Data Processing Libraries: NumPy, Pandas, scikit-learn, and OpenCV.
• Data Storage: SQLite3 for local storage and MongoDB for cloud simulation.

8.2 Cryptographic parameter selection

The cryptographic parameters were selected to balance the security, computational efficiency, and numerical precision required for encrypted-domain biometric matching.

• Kyber-1024 (ML-KEM): Provides NIST Level-5 post-quantum security for session key encapsulation.
• Polynomial modulus degree ( n = 8192 ): Ensures approximately 128-bit classical security while supporting efficient SIMD packing.
• Coefficient modulus chain [60, 40, 40, 40, 38]: Enables the required multiplicative depth for encrypted squared Euclidean distance computation.
• Scaling factor ( 2 40 ): Maintains sufficient numerical precision for approximate arithmetic operations in CKKS.

8.3 CKKS noise growth and precision analysis

The CKKS scheme performs approximate arithmetic, where the ciphertext noise and scaling factors influence the numerical precision during homomorphic evaluation. In the proposed system, the multiplicative depth is limited to three, corresponding to the operations required for the squared Euclidean distance calculation.

8.3.1 Noise growth

Each ciphertext multiplication increases the noise, whereas the rescaling operations reduce the modulus and control the noise magnitude. The selected modulus chain [60, 40, 40, 40, 38] ensures that a sufficient noise budget remains after evaluation to allow for correct decryption.

8.3.2 Precision management

A scaling factor of 2 40 was used to maintain the precision across homomorphic operations. After each multiplication, rescaling aligns the ciphertext levels and prevents the uncontrolled growth of approximation errors.

8.3.3 Error bound

Let d ̃ 2 denote the decrypted approximate distance and d 2 denote the true distance. The CKKS approximation introduces an error term ϵ such thatwhere τ is the authentication threshold. The parameter selection ensures that ϵ remains sufficiently small to avoid affecting authentication decisions.

d ̃ 2 = d 2 + ϵ , | ϵ | ≪ τ 2

8.3.4 Impact on authentication accuracy

The experimental results (Section 10) show that the approximation error does not significantly affect the FAR, FRR, or EER. This confirms that the selected CKKS parameters achieved a suitable balance between computational efficiency and numerical precision.

Overall, the selected parameter configuration ensured that the noise growth remained bounded and that the approximation errors did not degrade the biometric-matching accuracy within the evaluated operating range. These guarantees hold under the assumption that the ciphertext noise remains within the decryption correctness bound imposed by CKKS parameterization.

8.4 Dataset and preprocessing

The evaluation used three publicly available biometric datasets.

• Face: PolyU Face Database
• Iris: IIT Delhi Iris Database
• Fingerprint: PolyU Fingerprint Database

The preprocessing steps included the following:

• Face alignment and normalization using OpenCV-based landmark detection
• Iris segmentation using Daugman’s rubber-sheet model
• Fingerprint minutiae extraction (ridge endings and bifurcations)

The extracted features were concatenated into a unified multimodal vector prior to the GA-based feature selection.

8.5 Adversarial evaluation setup

To evaluate the robustness of the authentication framework against adversarial attacks, synthetic biometric perturbations were generated using generative adversarial network (GAN) techniques applied to the PolyU face dataset [69]. A total of 500 synthetic spoof samples were generated and evaluated for each experimental configuration.

All spoofing experiments were conducted at the operating threshold corresponding to an Equal Error Rate (EER) of 0.2%, determined through Receiver Operating Characteristic (ROC) analysis of genuine and impostor authentication trials.

The Spoof Acceptance Rate (SAR) is defined as the proportion of adversarial samples incorrectly accepted by the authentication system at a fixed operating threshold. Unlike the False Acceptance Rate (FAR), which measures zero-effort impostor attempts, SAR captures targeted adversarial attack scenarios.

The following configurations were evaluated in this study.

• Single-modal face authentication
• Multimodal authentication without encryption
• Proposed Kyber + FHE multimodal system

Authentication decisions are computed using the encrypted squared Euclidean distance, CKKS.

9 Experimental design

This section defines the evaluation methodology, baseline systems, and performance metrics used to assess the effectiveness and robustness of the proposed post-quantum privacy-preserving multimodal biometric authentication framework.

9.1 Baseline systems

To isolate the contribution of each component, the proposed system was compared with the following baseline configurations.

• Plaintext Multimodal System: A conventional multimodal biometric system without encryption, serving as an upper-bound reference for accuracy and computational performance.
• CKKS without GA: A privacy-preserving system using CKKS encryption without GA-based feature selection, used to evaluate the impact of feature dimensionality on encrypted-domain computation.
• Single-Modal System: Biometric authentication using individual modalities without fusion, used to assess the contribution of multimodal fusion to robustness and accuracy.

These baselines enable controlled comparisons across the encryption, feature optimization, and multimodal fusion components of the model.

9.2 Evaluation metrics

The performance was evaluated using standard biometric authentication metrics.

• False Acceptance Rate (FAR)
• False Rejection Rate (FRR)
• Equal Error Rate (EER)

Additionally, the Spoof Acceptance Rate (SAR) is used to evaluate the robustness against adversarial biometric attacks, whereas the computational latency and encryption overhead are measured to assess practical feasibility.

9.3 Evaluation protocol

The implementation details are provided in Section 8. All systems were evaluated under identical conditions using the same datasets and preprocessing pipelines to ensure a fair comparison.

For experimental evaluation, the biometric dataset was partitioned into separate training, validation, and testing subsets to avoid data leakage during threshold selection and performance evaluation. The training subset was used for GA-based feature optimization and parameter tuning, whereas the validation subset was used for ROC-based threshold determination. Final FAR, FRR, EER, and robustness evaluations were conducted exclusively on the independent testing subset. The reported scalability experiments involving up to 5,000 authentication comparisons were performed using the testing configuration after threshold selection had been finalized.

The evaluation followed a consistent workflow as described below.

• Feature extraction from biometric inputs
• GA-based feature selection (when applicable)
• Feature-level fusion for multimodal systems
• Encryption using CKKS for privacy-preserving configurations
• Encrypted-domain similarity computation
• Threshold-based authentication decision using ROC-derived thresholds

All experimental parameters were kept constant across the baseline and proposed systems, unless explicitly varied for ablation analysis, ensuring reproducibility and controlled comparison.

10 Performance evaluation and benchmarking

The results of the proposed authentication framework are summarized in Tables 10, 11 and 19 and in Figures 5, 6. The evaluation considers biometric authentication performance (FAR, FRR, and EER), cryptographic latency, homomorphic computation overhead, adversarial resistance, and system scalability issues.

TABLE 10. Performance summary of the proposed authentication system.

TABLE 11. Comparative analysis of the proposed framework against recent post-quantum biometric authentication schemes.

Owing to the limited number of published frameworks that simultaneously integrate standardized post-quantum cryptography, homomorphic encryption, and multimodal biometric authentication, the comparison includes the most relevant and closely related state-of-the-art post-quantum biometric authentication frameworks. Performance metrics are reported exactly as presented in the original publications to ensure fair and transparent comparison. NR (Not Reported) indicates that the corresponding metric was not explicitly provided in the original publication.

10.1 Practical scalability and deployment considerations

Although the proposed framework incorporates computationally intensive fully homomorphic encryption, the experimental results demonstrate that practical encrypted-domain biometric authentication can be achieved with acceptable latency for security-critical applications. The measured end-to-end authentication latency of approximately 65–75 ms per query indicates that the proposed architecture is suitable for applications such as secure healthcare systems, enterprise identity management, cloud-based authentication services, and critical infrastructure, where strong privacy guarantees are prioritized over ultra-low-latency operation.

The principal computational overhead arises from CKKS homomorphic evaluation, particularly ciphertext multiplication, rotation, and rescaling operations required during encrypted similarity computation. Consequently, the proposed framework may not be directly suitable for highly resource-constrained embedded devices or battery-powered edge platforms where computational resources, memory capacity, and energy consumption are severely limited. In such environments, computationally intensive homomorphic operations can be offloaded to trusted cloud or edge servers while preserving biometric confidentiality through end-to-end encrypted-domain processing.

From a scalability perspective, several architectural optimizations improve the practicality of the proposed framework. First, SIMD batching enables multiple biometric feature components to be processed simultaneously within a single ciphertext, thereby substantially reducing the effective computational overhead per authentication query. Second, the GA-based feature selection mechanism reduces the biometric feature dimensionality prior to encryption, decreasing ciphertext size, memory consumption, and homomorphic computation. Experimental evaluation demonstrated successful authentication for up to 5,000 enrolled users while maintaining stable authentication performance.

Although fully homomorphic encryption inevitably introduces greater computational overhead than conventional plaintext biometric authentication systems, the proposed framework represents a practical compromise between quantum-resistant security, privacy preservation, authentication accuracy, and computational efficiency. Therefore, the proposed architecture is particularly well suited for security-sensitive applications in which confidentiality and long-term quantum resilience outweigh the additional computational cost associated with encrypted-domain biometric processing.

10.2 Comparative evaluation with recent state-of-the-art post-quantum biometric authentication frameworks

To comprehensively evaluate the effectiveness of the proposed framework, a comparative analysis was conducted against recent state-of-the-art post-quantum biometric authentication frameworks reported in the literature. The selected studies represent closely related approaches that employ post-quantum cryptography, homomorphic encryption, secure biometric template protection, or post-quantum multi-factor authentication. Specifically, the proposed framework is compared with the privacy-preserving multimodal biometric recognition framework of [70], the homomorphic McEliece-based biometric authentication scheme proposed by [42], the RLWE-based cancelable biometric authentication framework introduced by [71], and the post-quantum multi-factor authentication protocol for the Medical Internet of Things (MIoT) developed by [32]. These frameworks represent the most closely related state-of-the-art approaches currently available for benchmarking the proposed architecture.

Table 11 summarizes the comparison across key technical and performance characteristics, including the underlying post-quantum cryptographic algorithm, homomorphic encryption scheme, biometric modality, authentication performance, execution time, key size or storage overhead, security level, strengths, and limitations. Owing to the limited number of published frameworks that simultaneously integrate standardized post-quantum cryptography, homomorphic encryption, and multimodal biometric authentication, the selected studies provide an appropriate benchmark for evaluating the proposed framework. All reported performance metrics were obtained directly from the corresponding publications to ensure consistency and fairness in the comparative evaluation.

Table 11 demonstrates that the proposed framework achieves a balanced trade-off between authentication performance, computational efficiency, privacy preservation, and post-quantum security. Although the proposed framework exhibits a moderately higher execution time than several of the compared approaches, this additional computational overhead is expected because the framework simultaneously performs feature-level fusion of three complementary biometric modalities (face, iris, and fingerprint) within the encrypted domain using CKKS homomorphic encryption while employing the NIST-standardized ML-KEM (Kyber-1024) for quantum-resistant key establishment. Consequently, the measured execution time reflects the additional processing required to preserve biometric privacy throughout the authentication process rather than conventional plaintext biometric matching.

Compared with the existing frameworks, the proposed approach provides a more comprehensive authentication architecture. [70] combine post-quantum cryptography with homomorphic encryption for multimodal biometric recognition using retina and palm vein biometrics, whereas the proposed framework extends encrypted feature-level fusion to three complementary biometric modalities. References [42, 71] focus on single-modal biometric authentication, while [32] propose a post-quantum multi-factor authentication protocol for MIoT environments without encrypted-domain biometric matching. Furthermore, the proposed framework adopts the standardized NIST ML-KEM algorithm for quantum-resistant key establishment while integrating CKKS homomorphic encryption and multimodal biometric fusion into a unified authentication framework.

Overall, the comparative evaluation demonstrates that the proposed framework provides a practical balance between authentication accuracy, post-quantum security, biometric privacy, and computational performance. While several existing approaches achieve lower execution times by employing unimodal biometrics or omitting encrypted-domain multimodal processing, the proposed framework uniquely integrates standardized post-quantum cryptography, homomorphic encryption, and feature-level fusion of three biometric modalities within a single authentication architecture. These characteristics make the proposed framework particularly suitable for high-security applications requiring long-term cryptographic resilience, privacy-preserving biometric authentication, and robust recognition performance.

10.3 Biometric authentication performance

The authentication performance of the proposed multimodal biometric system was benchmarked against that of a single-modal system (Figure 7) using the error metrics defined in Table 12. The quantitative results are presented in Table 10.

TABLE 12. Biometric error metrics and their significance.

The multimodal system achieved an Equal Error Rate (EER) of 0.2% and a False Rejection Rate (FRR) of 0.4%. No false acceptance events were observed during the 250,000 impostor trials conducted in this study. Accordingly, the FAR should be interpreted as < 0.0015 % (95% confidence upper bound) under finite-sample evaluation conditions rather than as an absolute zero probability.

Empirical validation:

• No false acceptance events observed in 250,000 impostor trials
• FRR = 0.4%
• EER = 0.2%

Owing to the inherent class imbalance in biometric authentication evaluation protocols, the FAR, FRR, and EER provide more meaningful performance indicators than overall classification accuracy.

10.3.1 Threshold sensitivity analysis

The authentication threshold τ is derived from the ROC analysis to balance the FAR and FRR at the equal error rate (EER) operating point. Small variations in τ around this operating point result in predictable trade-offs: decreasing τ reduces FAR at the cost of increased FRR, while increasing τ improves usability but slightly increases acceptance risk. Experimental observations indicate that the proposed system maintains stable performance within a narrow threshold interval around the selected operating point, thereby demonstrating its robustness to moderate threshold perturbations.

10.4 Statistical interpretation of zero-event FAR estimation

In biometric authentication evaluation, the absence of observed false acceptance events does not imply an absolute zero False Acceptance Rate (FAR). Because FAR estimation depends on finite sampling, zero-event observations were interpreted using confidence-bound estimation rather than deterministic zero-probability assumptions.

Specifically, the FAR confidence bound was estimated using an exact binomial approximation under 250,000 impostor authentication trials. Given zero observed false acceptance events, the upper 95% confidence bound on the FAR was approximately 0.0015%. Therefore, the reported FAR values should be interpreted as empirical upper-bound estimates under finite sampling conditions rather than absolute guarantees of zero false acceptance probability.

10.4.1 Receiver operating characteristic (ROC) analysis

To evaluate the discriminative capability of the proposed authentication system, ROC analysis was performed by sweeping the decision threshold τ across the full empirical range of the similarity score. Unlike narrow threshold sweeps that can produce degenerate behavior, this approach ensures an accurate characterization of the trade-off between the False Acceptance Rate (FAR) and True Positive Rate (TPR).

The resulting ROC curves exhibited strong separability between the genuine and impostor score distributions (Figure 7). Under clean biometric conditions, the system achieved near-perfect separation, with an Equal Error Rate (EER) near-perfect discriminative separability. Under noisy conditions, biometric variability introduced a partial overlap, resulting in an operational EER of approximately 0.2%, which is consistent with Table 10. The absence of false acceptances across 250,000 impostor trials further supports the robustness of the proposed system.

To quantify this behavior, the Area Under the Curve (AUC) was computed from the empirical ROC curves. The clean-condition ROC achieved an AUC of 1.0, whereas the noisy-condition ROC yielded an AUC of approximately 0.998, reflecting minor degradation owing to perturbations and CKKS approximation.

As shown in Figure 7, this dual evaluation distinguishes intrinsic model separability from practical deployment. The observed sensitivity under noisy conditions is consistent with CKKS-based approximate arithmetic, where perturbations and accumulated approximation noise can affect the similarity score stability without compromising the cryptographic confidentiality.

10.4.2 Computation of FAR, FRR, and EER

Let G denote the number of genuine authentication attempts and I the number of impostor attempts. For each authentication trial, the homomorphically computed squared distance is decrypted as a scalar value d 2 and compared with threshold τ 2.

T P = number of genuine attempts correctly accepted

F N = number of genuine attempts incorrectly rejected

T N = number of impostor attempts correctly rejected

F P = number of impostor attempts incorrectly accepted

where I = F P + T N and G = T P + F N.

The False Acceptance Rate (FAR) and False Rejection Rate (FRR) are defined as

F A R = F P I , F R R = F N G

The Equal Error Rate (EER) is obtained by varying the decision threshold τ and identifying the point where

F A R τ = F R R τ

At the selected operating threshold corresponding to EER = 0.2%, the system produced the following results:

F R R = 0.4 %

No false acceptance events were observed in the 250,000 impostor trials conducted during the evaluation. The corresponding authentication outcomes, including the numbers of true positives, false negatives, true negatives, and false positives used to compute the evaluation metrics, are summarized in Table 13.

TABLE 13. Authentication outcome breakdown.

All error metrics were computed after the encrypted domain similarity evaluation, ensuring that the biometric templates remained encrypted throughout the matching process.

All error metrics were computed after the encrypted domain similarity evaluation, ensuring that the biometric templates remained encrypted throughout the matching process.

The breakdown confirms the consistency between the empirical counts and reported FAR, FRR, and accuracy values.

Metric Verification:

F A R = F P I = 0 250000

No false acceptance events were observed during the conducted impostor trials. Accordingly, the FAR should be interpreted as an empirical upper-bound estimate under finite sampling conditions, corresponding to an approximate upper 95% confidence bound of < 0.0015 %.

F R R = F N G = 20 5000 = 0.4 %

Accuracy = T P + T N T P + T N + F P + F N = 4980 + 250000 255000 ≈ 99.99 %

10.5 Robustness under noise variations

The results presented in Table 14 provide an empirical basis for computing the authentication performance metrics, including the FAR, FRR, and EER, under varying noise conditions.

TABLE 14. System robustness summary across noise levels.

A controlled sample of 500 genuine multimodal biometric samples was used to evaluate the robustness of the proposed system. Independent perturbations were applied to these samples across noise levels ranging from 0.1% to 2%, generating 500 genuine authentication trials at each noise level.

For the impostor evaluation, each perturbed sample was compared with 500 non-matching templates, resulting in impostor comparisons per noise level. Across the ten noise levels, this resulted in 2.5 million impostor comparisons.

500 × 500 = 250,000

Table 14 summarizes the system performances for all evaluated noise levels.

Across the 250,000 impostor trials conducted at each noise level, no false acceptance events were observed, resulting in an empirical FAR of zero within the experimental resolution. The False Rejection Rate (FRR) remained below 0.4% even under the highest perturbation levels.

The Genuine Acceptance Rate GAR (=1 − F R R) remained at or above 99.6% across all evaluated noise levels.

These results confirm that the proposed system maintains stable authentication performance under increasing perturbations. The minimal variation in the optimal threshold across noise levels further indicates the robustness of the similarity score distribution and the stability of the decision boundary under encrypted-domain processing.

As shown in Table 14, the system maintained consistently low error rates at all noise levels. The absence of false acceptance events demonstrates a strong resistance to impostor attacks, whereas the bounded FRR ensures high usability.

Furthermore, the stability of the decision threshold across varying noise conditions indicates that noise-induced perturbations and CKKS approximation effects do not significantly affect the separability between genuine and imposter-score distributions.

These empirical results form the basis of the ROC analysis presented in Section 10.4.1.

Observed metric variations across repeated robustness evaluations remained within narrow empirical confidence ranges, indicating stable authentication behavior under incremental noise perturbations. Although small fluctuations were observed across different noise conditions, the overall FAR, FRR, and GAR trends remained consistent throughout the evaluated range, supporting the robustness and stability of the proposed framework under moderate biometric perturbations.

Because robustness evaluation involved repeated comparisons across 10 different noise levels, a conservative Bonferroni-style interpretive approach [72] was adopted to reduce the potential risk of Type I errors (false positives) arising from multiple evaluations. Accordingly, the robustness analysis focused primarily on consistent overall performance trends across noise conditions rather than isolated fluctuations observed at individual noise levels.

10.6 Genetic algorithm-based feature selection performance

The GA-based feature selection reduced the biometric template dimensionality from 95 to 45 features while preserving the authentication performance. This dimensionality reduction decreases the storage overhead and reduces the encrypted domain computation cost.

10.7 Fully homomorphic encryption benchmarking

Figure 5 summarizes the performance of the system after applying fully homomorphic encryption to biometric matching. Figure 8 illustrates the computational overhead introduced by homomorphic evaluation relative to classical template matching.

Although homomorphic encryption increases authentication latency compared with plaintext matching, batching, and SIMD packing significantly reduce the overhead.

10.8 Adversarial AI and deepfake attack evaluation

The proposed framework was further evaluated under adversarial conditions using GAN-generated biometric spoofing attempts to assess its robustness. Unlike single-modal biometric systems, which are vulnerable to facial manipulation attacks, the proposed multimodal encrypted-domain architecture introduces structural protection at both the biometric and cryptographic levels.

10.8.1 Results and observations

Figure 9 shows the spoof acceptance rates observed for different authentication configurations.

The single-modal face authentication system exhibited a Spoof Acceptance Rate (SAR) of 18.6%. Multimodal fusion without encryption reduced the SAR to 6.3%. The proposed encrypted multimodal architecture further reduced the adversarial success to 0.8% at the operating threshold corresponding to EER = 0.2%.

These observations indicate that multimodal biometric fusion significantly improves spoof resistance, whereas encrypted domain processing further strengthens adversarial resilience.

10.9 Scalability and deployment feasibility

Scalability was experimentally evaluated for user populations of up to 5,000 by analyzing authentication latency and system resource utilization (Figures 5, 10). The results indicate that the authentication latency remains stable under an increasing workload, whereas the resource utilization scales are predictable. These findings demonstrate that the proposed architecture can effectively support large-scale deployments when combined with batching and parallel processing techniques.

10.10 Comparison with classical authentication systems

To highlight the advantages of the proposed framework, we compared it with conventional authentication systems based on classical cryptography and biometric plaintext processing.

Table 15 presents a comparative analysis of classical and proposed authentication systems across security, privacy, and robustness dimensions.

TABLE 15. Comparison of classical vs. proposed authentication systems.

The comparison shows that the proposed framework significantly improves privacy, spoof resistance, and quantum security while maintaining a strong authentication performance through multimodal fusion and encrypted-domain processing.

10.11 Comparison of CKKS with alternative homomorphic schemes

The CKKS scheme was compared with alternative homomorphic encryption approaches to demonstrate its suitability for biometric matching.

Table 16 summarizes the differences between CKKS and other commonly used homomorphic encryption schemes.

TABLE 16. Comparison of CKKS with other homomorphic encryption schemes.

The comparison indicates that CKKS is the most appropriate choice for biometric systems because it supports efficient approximate arithmetic over real-valued feature vectors, thereby enabling practical encrypted-domain similarity computation.

10.11.1 Summary of communication and storage costs

Table 17 summarizes the communication and storage overhead introduced by the proposed system.

TABLE 17. Communication and storage overhead of the proposed framework.

id = “evalkey1” Evaluation keys introduce additional memory overhead; however, this cost is amortized across all users because the same keys are reused for homomorphic operations across the authentication queries.

10.11.2 Kyber communication overhead

Kyber-1024 produces ciphertexts of approximately 1.5 KB per encapsulation. This ciphertext is transmitted during session key establishment and is independent of the biometric data size.

10.11.3 FHE ciphertext size

Under the CKKS configuration ( n = 8192 ), each ciphertext occupies approximately 16–32 kB, depending on the modulus chain and scaling parameters. Because biometric feature vectors are SIMD-packed into a single ciphertext, each authentication query requires the transmission of one encrypted query vector.

10.11.4 Storage overhead per user

Each enrolled user requires the storage of.

• One encrypted biometric template (≈ 16–32 KB)
• Associated metadata and indexing information

Thus, the storage requirements scale linearly with the number of user. For example, a system with 100,000 users would require approximately 1.6–3.2 GB of encrypted template storage.

10.11.5 Insights

Although the proposed system incurs higher storage and communication costs than plaintext biometric systems, these overheads are justified by the strong privacy guarantees and quantum-resistant security properties of the proposed system. Furthermore, batching and SIMD packing reduce the effective communication costs for each authentication query.

10.11.5.1 Latency interpretation

The reported CKKS similarity computation latency of 5.23 s corresponds to a non-batched primitive-level evaluation of a single encrypted comparison. In contrast, the end-to-end authentication latency of 65–75 ms reflects the amortized performance achieved through SIMD batching, parallel execution, and feature dimensionality reduction, enabling multiple encrypted comparisons to be processed concurrently. These measurements therefore represent different operational granularities within the authentication pipeline and should not be interpreted as directly equivalent latency metrics.

11 Ablation study

This section analyzes the contributions of individual components of the proposed authentication framework, including GA-based feature selection, multimodal fusion, and encrypted-domain computation. The objective was to isolate the impact of each component on authentication accuracy, robustness, and computational performance.

11.1 Effect of GA-based feature selection

To evaluate the impact of GA-based feature selection, we compared the system performance with and without the dimensionality reduction.

Without GA optimization, the fused feature vector contains 95 dimensions, resulting in an increased computational overhead during the CKKS-based homomorphic evaluation. With GA-based feature selection, the feature dimensionality was reduced to 45 while preserving the discriminative information.

Observation:

• GA-based feature selection reduces computational complexity and ciphertext size.
• Encrypted-domain evaluation becomes more efficient due to lower multiplicative cost.
• Authentication accuracy (EER) remains stable, indicating that redundant features are effectively removed without degrading performance.

11.1.1 Conclusion

GA-based feature selection improves efficiency while maintaining authentication accuracy, making it well-suited for homomorphic biometric matching.

11.2 Effect of multimodal fusion

To assess the contribution of multimodal fusion, we compared the single-modal and multimodal configurations.

Compared configurations:

• Face-only authentication
• Multimodal authentication (face + iris + fingerprint)

Observation:

• Single-modal systems exhibit higher susceptibility to spoofing attacks, with significantly higher Spoof Acceptance Rate (SAR).
• Multimodal fusion reduces SAR substantially (e.g., from 18.6% in single-modal to 0.8% in the proposed system).
• Equal Error Rate (EER) improves due to complementary information across modalities.

11.2.1 Conclusion

Multimodal fusion significantly enhances robustness against adversarial attacks and improves authentication reliability.

11.3 Effect of encrypted-domain computation

To evaluate the impact of encryption, we compared plaintext and CKKS-based encrypted domain authentication.

Compared configurations:

• Plaintext multimodal system
• CKKS-based encrypted multimodal system

Observation:

• Encrypted-domain computation introduces additional computational latency due to homomorphic operations.
• Authentication accuracy (FAR, FRR, EER) remains comparable to the plaintext system, indicating minimal impact from approximation error.
• Biometric templates remain protected during both storage and computation, significantly improving privacy and security.

11.3.1 Conclusion

CKKS-based encrypted-domain matching achieves strong privacy guarantees with acceptable computational overhead and negligible impact on authentication performance.

11.4 Effect of post-quantum key encapsulation (Kyber)

To evaluate the impact of post-quantum key establishment, we compared the proposed Kyber-based approach with a baseline classical key-exchange mechanism.

Compared configurations:

• Classical key exchange (e.g., RSA or ECC-based)
• Post-quantum key encapsulation using Kyber-1024

Observation:

• Kyber introduces minimal computational overhead (4.5 ms encapsulation latency) compared to classical key exchange mechanisms, with encapsulation latency remaining within practical limits.
• Session keys derived using Kyber provide quantum-resistant security under the MLWE assumption.
• No impact on biometric matching accuracy (FAR, FRR, EER) is observed, as key exchange operates independently from biometric processing.

11.4.1 Conclusion

The use of Kyber enables quantum-resistant secure communication with negligible performance overhead, ensuring long-term security without affecting authentication accuracy.

11.5 Summary of component contributions

The ablation results demonstrated the following:

• GA-based feature selection improves computational efficiency by reducing feature dimensionality without degrading authentication accuracy.
• Multimodal fusion enhances robustness by significantly reducing spoofing vulnerability and improving overall authentication reliability.
• Encrypted-domain computation using CKKS preserves biometric privacy during both storage and matching, with minimal impact on authentication performance.
• Post-quantum key encapsulation using Kyber provides quantum-resistant secure communication with negligible computational overhead, ensuring long-term security without affecting biometric matching accuracy.

11.6 Summary of ablation results

Table 18 summarizes the impact of the key components of the proposed system, including GA-based feature selection, multimodal fusion, and encrypted domain computation.

TABLE 18. Ablation study summary showing EER, FRR, and SAR performance across Configurations with corresponding 95% confidence intervals (CI).

Although the observed improvements in EER, FRR, and SAR across the evaluated configurations were relatively small in absolute magnitude, the proposed framework consistently demonstrated improved authentication performance under identical experimental conditions. Because the evaluation involved large authentication sample sizes, the reported metrics were interpreted using confidence-based statistical reasoning rather than isolated point estimates. Therefore, the improvements observed in the proposed multimodal GA + CKKS configuration should be interpreted as consistent empirical performance gains rather than absolute deterministic superiority.

The ablation results demonstrated that each component contributed incrementally to the overall performance of the system. Multimodal fusion yielded the most significant improvement by substantially reducing the error rates and enhancing robustness against spoofing attacks. GA-based feature selection improves computational efficiency while maintaining comparable accuracy. The integration of CKKS-based encrypted-domain computation preserves authentication performance while ensuring strong privacy guarantees. Additionally, the use of Kyber (ML-KEM) enables secure and quantum-resistant session key establishment, protecting the transmission of cryptographic artifacts without introducing a significant overhead.

Overall, the combination of multimodal fusion, feature optimization, homomorphic encryption, and post-quantum key encapsulation achieves a balanced trade-off between security, accuracy, privacy, and computational feasibility, resulting in a robust and practically deployable post-quantum biometric authentication framework.

12 Practical security evaluation

This section complements the formal analysis presented in Section 6 by evaluating the practical security properties of the proposed framework in real-world scenarios. Although formal analysis establishes security guarantees under standard cryptographic assumptions (MLWE and RLWE), this section focuses on system-level resilience against concrete adversarial threats.

The proposed framework is designed to mitigate a wide range of attack vectors, including quantum cryptanalysis, template inversion, replay attacks, adversarial AI-based spoofing, and database compromise. These threats were evaluated in the context of the implemented system architecture and the experimental observations.

12.1 System-level security properties

The framework ensures the following practical security properties:

• Quantum-resistant communication: The use of ML-KEM (Kyber-1024) provides secure session key establishment resistant to harvest-now-decrypt-later attacks, ensuring long-term confidentiality of transmitted data.
• Encrypted biometric processing: Biometric templates remain encrypted under CKKS during both storage and computation, preventing exposure of sensitive biometric information.
• Replay resistance: Authentication relies on fresh biometric inputs and session-specific cryptographic operations, preventing reuse of previously captured data.
• Adversarial robustness: Multimodal biometric fusion significantly reduces susceptibility to spoofing and adversarial AI attacks, as demonstrated in the experimental evaluation.
• Database breach resilience: Even in the event of database compromise, encrypted templates remain computationally infeasible to reverse without access to the FHE secret key.
• Side-channel awareness: The framework reduces exposure of sensitive biometric data during computation; however, secure deployment requires constant-time implementations and hardened cryptographic libraries.

12.2 Leakage considerations in CKKS-based matching

Although CKKS enables privacy-preserving computation over encrypted biometric data, it inherently supports approximate arithmetic, which may introduce subtle information leakage through repeated query interactions.

12.2.1 Approximation leakage

CKKS ciphertexts encode approximate real-valued computations. While ciphertexts remain IND-CPA secure under the RLWE assumption (Section 3), the decrypted similarity score d 2 is revealed to the server for decision-making. Repeated evaluations may allow an adversary to infer the relative distances between biometric templates using statistical analysis.

12.2.2 Threshold-based leakage

The authentication decision is based on a threshold comparison d 2 ≤ τ 2. An adaptive adversary issuing multiple queries may approximate the decision boundary by observing accept/reject responses, potentially enabling distance inference or template proximity estimation.

12.2.3 Membership inference risk

Repeated probing with crafted biometric inputs may allow an adversary to infer whether a specific biometric template exists in the database, leading to potential linkability or membership inference attacks.

12.2.4 Mitigation strategies

To reduce the risk of leakage, the system can incorporate the following measures:

• Query rate limiting and access monitoring to prevent adaptive probing,
• Randomized response mechanisms or noise injection near the decision boundary,
• Threshold randomization or secure comparison protocols,
• Auditing and anomaly detection for repeated authentication attempts.

These considerations demonstrate that although CKKS provides strong cryptographic confidentiality under standard RLWE-based assumptions, additional system-level protections remain necessary to reduce inference-based privacy risks arising from repeated authentication interactions. In particular, decrypted similarity scores may leak limited auxiliary information regarding biometric template proximity or score distributions when observed across multiple adaptive queries. Although direct reconstruction of biometric templates from encrypted CKKS representations remains computationally difficult, an adversary repeatedly observing similarity-score outputs could potentially infer partial statistical characteristics of underlying biometric templates or approximate decision-boundary behavior over time. Consequently, repeated-query strategies may increase susceptibility to membership inference, score-distribution profiling, or template approximation attacks under adversarial conditions. These leakage pathways were not experimentally evaluated in the present study and therefore represent important limitations of the current framework. Future work should investigate stronger leakage-resistant authentication mechanisms, differential privacy techniques, score obfuscation strategies, and verifiable encrypted inference protocols to further reduce inference-based privacy risks in practical large-scale deployments.

12.3 Security and attack resistance benchmarking

To evaluate practical resilience, the proposed system was compared with traditional authentication architectures based on classical cryptography and biometric plaintext processing.

Table 19 summarizes the comparative security properties of the proposed system for multiple-attack categories.

TABLE 19. Security comparison: proposed vs traditional systems.

Figure 11 illustrates the relative resistance of the proposed framework to classical and post-quantum adversarial attack.

13 Discussion

The analysis of the proposed post-quantum-secure biometric authentication framework provides insights into its performance characteristics, scalability, and practical deployment feasibility.

13.1 WAN latency interpretation and real-world feasibility

The optimized encapsulation latency was approximately 4.5 ms per session (Table 11). In typical wide-area network (WAN) environments, where the average network latency ranges between 30 and 50 ms, the cryptographic overhead represents only a small fraction of the total authentication handshake time. This indicates that the proposed framework is compatible with real-time deployment.

13.2 Cryptographic performance and real-time efficiency

Fully Homomorphic Encryption introduces additional computational costs compared with plaintext template matching. Primitive CKKS evaluation requires approximately 5.23 s per template when executed independently, corresponding to a non-batched single encrypted comparison. In contrast, the reported end-to-end system latency reflects the amortized performance achieved through batched and parallelized execution. System-level optimizations, including SIMD slot packing, GA-based feature dimensionality reduction, and multithreaded evaluation, enable multiple authentication computations to be processed concurrently. This distinction highlights the difference between isolated primitive-level cryptographic evaluation and optimized pipeline-level authentication performance in practical deployment scenarios.

Consequently, the effective end-to-end authentication latency within the integrated framework was approximately 65–75 ms per query under amortized batched execution. Although this latency remains higher than that of conventional plaintext biometric matching systems, the framework provides substantially stronger privacy guarantees by ensuring that biometric templates remain encrypted during both storage and computation.

Compared to prior homomorphic encryption-based biometric authentication systems, which report latencies ranging from several hundred milliseconds to multiple seconds per comparison depending on the system configuration and batching strategies [58], the proposed framework achieves a significantly improved practical performance through batching and parallelization. For example, systems such as HEFT report sub-second encrypted matching latency under optimized conditions [73]. In contrast, the proposed system achieves millisecond-level effective latency, enabling real-time deployment while preserving strong privacy guarantees.

While prior FHE-based systems, such as [21, 22] provide strong privacy guarantees, they typically incur higher computational overheads. In contrast, the proposed framework achieves practical real-time performance through batching and parallelization.

13.3 Authentication accuracy and biometric performance

Multimodal biometric fusion combined with GA-based feature selection preserves a strong discriminative capability, even under encrypted-domain computation. As reported in Section 10, the system achieved an Equal Error Rate (EER) of 0.2% and a False Rejection Rate (FRR) of 0.4%.

During the evaluation, which consisted of 250,000 impostor authentication attempts, no false acceptance events were detected. Because biometric authentication datasets typically contain a large imbalance between impostor and genuine attempts, performance is primarily assessed using the FAR, FRR, and EER rather than overall classification accuracy.

13.4 Robustness under noise variations

Table 14 demonstrates the stable system behavior under biometric perturbations ranging from 0.1% to 2%. Across all evaluated noise levels, no false acceptance events were observed in the 250,000 impostor trials for each of the noise levels.

The False Rejection Rate exhibited only minor variations under increased noise, remaining below 0.4% even at higher perturbation levels. The corresponding Genuine Acceptance Rate GAR ( 1 − F R R ) remained above 99.6% across all evaluated conditions. These results suggest that the encrypted-domain multimodal matching procedure maintains stable authentication performance under moderate biometric variability.

13.5 Scalability and real-time feasibility

The experimental evaluation was conducted for up to 5,000 user. Authentication latency remained stable under this workload because the Kyber encapsulation operated in constant time, and the CKKS similarity computation remained bounded under the selected parameter configuration. Resource utilization increased gradually with the user scale, indicating that the architecture can support larger deployments when parallel processing and distributed storage are employed.

13.6 Scalability analysis: validated, projected, and aspirational

To ensure methodological transparency, the scalability results were categorized into empirically validated, analytically projected, and aspirational performance levels.

• Validated (5k users): 65–75 ms per query based on empirical measurements.
• Projected (100k users): 75–90 ms per query assuming distributed batching and parallel CKKS evaluation.
• Aspirational (1M users): ≤120 ms per query assuming hardware acceleration and database sharding.

Table 20 summarizes the scalability levels.

TABLE 20. Scalability analysis of the proposed framework.

These projections assume ideal parallelization efficiency and do not account for potential network bottlenecks, synchronization overheads or resource contention in distributed environments. Therefore, the real-world performance at a larger scale may vary depending on the deployment architecture.

13.7 Computational overhead and trade-offs

Encrypted-domain biometric matching introduces additional computational overhead compared to classical template-matching. This overhead is a fundamental trade-off associated with the privacy-preserving computations. Hardware acceleration using GPU or FPGA platforms and improved batching strategies may significantly reduce homomorphic evaluation latency while preserving biometric privacy. In particular, the multiplicative depth of the CKKS circuit and associated rescaling operations significantly influence latency and resource consumption.

13.8 Practical deployment and ethical considerations

The real-world deployment of biometric authentication systems must consider privacy regulations, ethical data governance, and user consent. Compliance with biometric data protection standards and transparent governance frameworks is essential for ensuring the responsible deployment of secure authentication technologies. Additionally, the increasing prevalence of deepfake and synthetic biometric generation raises critical security concerns, further emphasizing the importance of multimodal authentication and encrypted domain processing for mitigating sophisticated spoofing attacks.

13.9 Side-channel and implementation-level risks

Although the proposed framework relies on cryptographic primitives with strong theoretical security guarantees, practical implementations may still be vulnerable to side-channel attacks. These attacks exploit information leakage through timing variations, power consumption, memory access patterns, and electromagnetic emissions.

In the context of the proposed system, both ML-KEM (Kyber) and CKKS-based homomorphic encryption may introduce potential leakage surfaces during the key encapsulation, ciphertext operations, and decryption. In particular, operations such as polynomial arithmetic, modular reductions, and ciphertext rotations may exhibit data-dependent execution behaviors if they are not carefully implemented.

Although biometric templates remain encrypted during storage and computation, side-channel leakage at the implementation level can expose sensitive intermediate values or cryptographic secrets. Recent studies have demonstrated practical side-channel vulnerabilities in lattice-based cryptographic implementations, highlighting the importance of constant-time polynomial arithmetic and secure memory access patterns. Therefore, secure deployment requires constant time implementations, masking techniques, and hardened cryptographic libraries.

Additionally, hardware-level protection, such as trusted execution environments (TEE) or secure enclaves, can further reduce exposure to side-channel threats. Future studies should include an empirical evaluation of the side-channel resistance under realistic attack models.

Overall, although the proposed architecture significantly reduces the direct exposure of biometric data, implementation-level security remains a critical consideration for real-world deployment.

13.10 Limitations

Despite their strong performance, several limitations must be considered. Fully Homomorphic Encryption introduces significant computational overhead. The evaluation is conducted in a simulation environment and may not fully reflect real-world deployment conditions. The current implementation does not incorporate GPU or FPGA acceleration. Implementation-level vulnerabilities such as side-channel attacks require further mitigation in practical deployments. CKKS introduces approximation error due to its inherent approximate arithmetic, which may impact precision in biometric similarity computations under certain parameter settings. Although 95% confidence intervals are reported for the primary biometric performance metrics, formal paired statistical significance testing across authentication configurations (e.g., McNemar’s test) was not performed in the present study and therefore remains an important direction for future statistical validation.

13.11 Future work

Future work will focus on improving efficiency and enabling real-world deployment. Hybrid BFV and CKKS integration for mixed-precision computation GPU/FPGA-based acceleration for homomorphic operations Edge and mobile deployment scenarios Large-scale real-world validation Enhanced side-channel resistant implementations Integration of deepfake detection mechanisms and adversarial robustness evaluation under adaptive attack models.

13.12 Validation of contributions

The experimental results and analyses presented in Sections 9–13 collectively validate the contributions outlined in Section 1. Specifically: The integration of ML-KEM and CKKS is validated through secure key establishment and encrypted-domain matching performance (Sections 10, 12). The effectiveness of GA-based feature selection is demonstrated through reduced dimensionality and improved computational efficiency (Section 11). The robustness of multimodal fusion is confirmed through reduced SAR and improved EER (Section 10). The feasibility of encrypted-domain biometric authentication is empirically validated through latency and scalability analysis (Sections 10, 13).

13.13 Summary of discussion

The proposed framework demonstrates that post-quantum-secure multimodal biometric authentication can achieve strong security, high accuracy, and practical performance when supported by system-level optimization techniques. Although Fully Homomorphic Encryption introduces computational overhead, techniques such as SIMD batching, feature dimensionality reduction, and parallel processing enable real-time authentication performance.

Overall, the results indicate that the integration of Kyber-based key establishment with encrypted-domain multimodal biometric matching provides a viable pathway toward privacy-preserving and quantum-resilient authentication systems suitable for high-security applications. This positions the proposed framework as a strong candidate for next-generation authentication systems in emerging post-quantum and AI-driven threat landscapes.

14 Reproducibility statement

The entire experimental parameters, cryptographic settings, and system settings employed in this study are clearly stated in the manuscript (Sections 7–9). This section provides detailed descriptions of the CKKS parameters, Kyber-1024 configuration, GA-based feature selection settings, and evaluation protocols.

The biometric datasets used in this study (PolyU Face [74], IITD Iris [75–77], and PolyU Fingerprint [78]) are publicly available and widely used benchmark datasets in biometric research database, [69, 79–81]. Every preprocessing step, feature extraction method, and fusion strategy is presented in detail to enable the independent replication of the study.

The implementation was performed using publicly available libraries, including Microsoft SEAL for fully homomorphic encryption and PQClean for post-quantum cryptographic primitives. All experiments were conducted using standardized and deterministic pipelines to ensure consistency between the baseline and proposed systems.

Additional implementation details, CKKS parameter configurations, evaluation protocols, statistical analysis procedures, and supplementary reproducibility materials are provided in the publicly accessible Supplementary Material accompanying this manuscript.

15 Conclusion

In this study, we proposed a post-quantum secure multimodal biometric authentication framework that integrates ML-KEM (Kyber-1024), CKKS-based fully homomorphic encryption, multimodal biometrics and GA-based feature optimization within a unified architecture. The proposed system enables privacy-preserving authentication by ensuring that biometric templates remain encrypted during both storage and computation, while simultaneously providing resilience against quantum-enabled cryptographic attacks.

Unlike prior approaches that treat cryptographic protection and biometric processing independently, the proposed framework combines post-quantum key establishment with encrypted-domain multimodal biometric matching in a cohesive and end-to-end pipeline. The incorporation of GA-based feature selection further improves computational efficiency by reducing feature dimensionality while preserving discriminative performance.

Experimental evaluation demonstrated strong performance, with no false acceptances observed across 250,000 impostor trials, corresponding to an empirical FAR upper bound of approximately 0.0015% at the 95% confidence level. The framework additionally achieved an Equal Error Rate (EER) of 0.2%, a False Rejection Rate (FRR) of 0.4%, and a Spoof Acceptance Rate (SAR) of 0.8%. The framework supports validated scalability evaluations involving up to 5,000 identities, with an effective authentication latency of 65–75 ms per query under amortized batched execution. Robustness analysis under biometric perturbations of up to 2% confirmed stable authentication performance under realistic conditions.

These results demonstrate that strong privacy guarantees, high authentication accuracy, robustness against spoofing attacks, and quantum-resistant security can be achieved simultaneously in a single system. Although fully homomorphic encryption introduces computational overhead, system-level optimizations such as SIMD batching, feature reduction, and parallel processing enable practical real-time deployment.

Overall, this study establishes a viable pathway toward next-generation authentication systems that are secure against both quantum and AI-driven threats. By bridging post-quantum cryptography, encrypted-domain computation, and multimodal biometrics, the proposed framework provides a strong foundation for secure digital identity systems in high-security applications.

Generative AI statement

The author(s) declared that generative AI was used in the creation of this manuscript. During the preparation of this study, we used ChatGPT to improve the readability and language of the manuscript. After using this tool, the authors reviewed and edited the content as needed and took full responsibility for the published content.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphy.2026.1849257/full#supplementary-material

Supplementary material Supplementary material at the source

Footnotes

Edited by: Umar Khokhar, Georgia Gwinnett College, United States

Reviewed by: Aarthi S, SRM Institute of Science and Technology, India

Shri Kant, Sharda University, India

Zainab Dhahir, Al-Furat Al-Awsat Technical University, Iraq