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In contemporary digital security systems, the generation and management of cryptographic keys, such as passwords and pin codes, often rely on stochastic random processes and intricate mathematical transformations. While these keys ensure robust security, their storage and distribution necessitate sophisticated and costly mechanisms. This study explores an alternative approach that leverages biometric data for generating cryptographic keys, thereby eliminating the need for complex storage and distribution processes. The paper investigates biometric key generation technologies based on deep learning models, specifically utilizing convolutional neural networks to extract biometric features from human facial images. Subsequently, code-based cryptographic extractors are employed to process the primary extracted features. The performance of various deep learning models and the extractor is evaluated by considering Type 1 and Type 2 errors. The optimized algorithm parameters yield an error rate of less than 10 % , rendering the generated keys suitable for biometric authentication. Additionally, this study demonstrates that the application of code-based cryptographic extractors provides a post-quantum level of security, further enhancing the practicality and effectiveness of biometric key generation technologies in modern information security systems. This research contributes to the ongoing efforts towards secure, efficient, and user-friendly authentication and encryption methods, harnessing the power of biometric data and deep learning techniques. [ABSTRACT FROM AUTHOR]

For Reed–Muller codes we consider subcodes of codimension 1. A classification of Hadamard products of such subcodes is obtained. With the use of this classification it has been shown that in most cases the problem of recovery of the secret key of a code-based cryptosystem employing such subcodes is equivalent to the problem of recovery of the secret key of the same cryptosystem based on Reed–Muller codes, which is known to be tractable. [ABSTRACT FROM AUTHOR]

In 1978, Robert McEliece constructed the first asymmetric code-based cryptosystem using noise-immune Goppa codes; no effective key attacks has been described for it yet. By now, quite a lot of code-based cryptosystems are known; however, their cryptographic security is inferior to that of the classical McEliece cryptosystem. In connection with the development of quantum computing, code-based cryptosystems are considered as an alternative to number theoretical ones; therefore, the problem of seeking promising classes of codes to construct new secure code-based cryptosystems is relevant. For this purpose, noncommutative codes can be used, that is, ideals in group algebras over finite noncommutative groups . The security of cryptosystems based on codes induced by subgroup codes has been studied earlier. The Artin–Wedderburn theorem, which proves the existence of an isomorphism of a group algebra to the direct sum of matrix algebras, is important for studying noncommutative codes. However, the particular form of terms and the construction of the isomorphism are not specified by this theorem; thus, for each group, there remains the problem of constructing the Wedderburn representation. The complete Wedderburn decomposition for the group algebra over the dihedral group has been obtained by F.E. Brochero Martinez in the case when the cardinality of the field and the order of the group are relatively prime numbers. Using these results, we study codes in the group algebra in this paper. The problem on the structure of all codes is solved, and the structure of codes induced by codes over cyclic subgroups of is described, which is of interest for cryptographic applications. [ABSTRACT FROM AUTHOR]

Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to be equally difficult tasks. Since the pioneering work of Eugene Prange in the early 1960s, a significant research effort has been put into finding more efficient methods to solve the random code decoding problem through a family of algorithms known as information set decoding. The obtained improvements effectively reduce the overall complexity, which was shown to decrease asymptotically at each optimization, while remaining substantially exponential in the number of errors to be either found or corrected. In this work, we provide a comprehensive survey of the information set decoding techniques, providing finite regime temporal and spatial complexities for them. We exploit these formulas to assess the effectiveness of the asymptotic speedups obtained by the improved information set decoding techniques when working with code parameters relevant for cryptographic purposes. We also delineate computational complexities taking into account the achievable speedup via quantum computers and similarly assess such speedups in the finite regime. To provide practical grounding to the choice of cryptographically relevant parameters, we employ as our validation suite the ones chosen by cryptosystems admitted to the second round of the ongoing standardization initiative promoted by the US National Institute of Standards and Technology.

We describe a family of efficient codes for cryptographic purposes and dedicated algorithms for their manipulation. Our proposal is especially tailored for highly constrained platforms, becoming competitive with conventional schemes. [ABSTRACT FROM AUTHOR]

Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to be equally difficult tasks. Since the pioneering work of Eugene Prange in the early 1960s, a significant research effort has been put into finding more efficient methods to solve the random code decoding problem through a family of algorithms known as information set decoding. The obtained improvements effectively reduce the overall complexity, which was shown to decrease asymptotically at each optimization, while remaining substantially exponential in the number of errors to be either found or corrected. In this work, we provide a comprehensive survey of the information set decoding techniques, providing finite regime temporal and spatial complexities for them. We exploit these formulas to assess the effectiveness of the asymptotic speedups obtained by the improved information set decoding techniques when working with code parameters relevant for cryptographic purposes. We also delineate computational complexities taking into account the achievable speedup via quantum computers and similarly assess such speedups in the finite regime. To provide practical grounding to the choice of cryptographically relevant parameters, we employ as our validation suite the ones chosen by cryptosystems admitted to the second round of the ongoing standardization initiative promoted by the US National Institute of Standards and Technology. [ABSTRACT FROM AUTHOR]