The multi-factor authentication (MFA) protocol requires users to provide a combination of a password, a smart card and biometric data as verification factors to gain access to the services they need. In a single-server MFA system, users accessing multiple distinct servers must register separately for each server, manage multiple smart cards, and remember numerous passwords. In contrast, an MFA system designed for multi-server architecture allows users to register once at a registration center (RC) and then access all associated servers with a single smart card and one password. MFA with an offline RC addresses the computational bottleneck and single-point failure issues associated with the RC. In this paper, we propose a post-quantum secure MFA protocol for a multi-server architecture with an offline RC. Our MFA protocol utilizes the post-quantum secure Kyber key encapsulation mechanism and an information-theoretically secure fuzzy extractor as its building blocks. We formally prove the post-quantum semantic security of our MFA protocol under the real or random (ROR) model in the random oracle paradigm. Compared to related protocols, our protocol achieves higher efficiency and maintains reasonable communication overhead.

A fuzzy extractor is a foundational cryptographic component that enables the extraction of reproducible and uniformly random strings from sources with inherent noise, such as biometric traits. Reusable fuzzy extractor guarantees the security of multiple extractions from the same noisy source. In addition, although isogeny-based cryptography has become an important branch in post-quantum cryptography, the study of fuzzy extractors based on isogeny assumptions is still in its early stages and holds much room for improvement. In this paper, we give two reusable fuzzy extractor schemes derived from isogeny-based assumptions: one is based on the linear hidden shift assumption over group actions, while the other is built upon the group-action decisional Diffie–Hellman assumption within the isogeny framework. Both proposed constructions achieve post-quantum security and are capable of correcting a linear proportion of errors. They rely solely on fundamental cryptographic primitives, which ensure simplicity and efficiency. Additionally, the second construction is based on restricted effective group action, which is weaker than the effective group action used in the first construction, thereby offering greater practical applicability.

Fuzzy signature (${\mathsf{SIG}}_{\mathsf{F}}$) is a type of digital signature that preserves the core functionalities of traditional signatures, while accommodating variations and non-uniformity in the signing key. This property enables the direct use of high-entropy fuzzy data, such as biometric information, as the signing key. In this paper, we define the m-existentially unforgeable under chosen message attack ($\mathfrak{m}{-\mathrm{EUF}-\mathrm{CMA}}^{\ast }$) security of fuzzy signature. Furthermore, we propose a generic construction of fuzzy signature, which is composed of a homomorphic secure sketch ($\mathsf{SS}$) with an error-recoverable property, a homomorphic average-case strong extractor ($\mathsf{Ext}$), and a homomorphic and key-shift* secure signature scheme ($\mathsf{SIG}$). By instantiating the foundational components, we present a $\mathfrak{m}{-\mathrm{EUF}-\mathrm{CMA}}^{\ast }$ secure fuzzy signature instantiation based on the Computational Diffie–Hellman (CDH) assumption over bilinear groups in the standard model.

Remote data backup technology avoids the risk of data loss and tampering, and has higher security compared to local data backup solutions. However, the data transmission channel for remote data backup is not secure, and the backup server cannot be fully trusted, so users usually encrypt the data before uploading it to the remote server. As a result, how to protect this encryption key is crucial. We design a User-Centric Design (UCD) data backup scheme based on multi-factor authentication to protect this encryption key. Our scheme utilizes a secret sharing scheme to divide the encryption key into three parts, which are stored in the laptop, the smart card, and the server. The encryption key can be easily reconstructed from any two parts with user’s private information password, identity and biometrics. As long as the biometrics has enough entropy, our scheme can resist replay attacks, impersonation user attacks, impersonation server attacks, malicious servers and offline password guessing attacks.