Abstract BIKE is a post-quantum public-key encryption scheme based on Moderate-Density Parity-Check (MDPC) codes, gaining significant attention for its small public key and ciphertext sizes. However, it suffers from several critical limitations, including the lack of precise theoretical bounds for estimating the Decryption Failure Rate (DFR) and its vulnerability to weak-key and near-codeword attacks. These shortcomings ultimately contributed to its failure to be selected for standardization. To address these challenges, we propose an enhanced variant of the BIKE cryptosystem based on semi-MDPC codes. We reduce the syndrome decoding problem for semi-MDPC codes to the Quasi-Cyclic Codeword Finding and Quasi-Cyclic Syndrome Decoding problems. The proposed scheme resists major attacks specific to BIKE, such as weak-key and near-codeword attacks, while also enabling a rigorous theoretical analysis of the DFR with provable upper bounds–significantly improving security and reliability. Furthermore, we introduce a block-cyclic matrix structure to enhance security and reduce ciphertext size at the cost of an increased public key size. Compared with McEliece, our scheme achieves significantly smaller key sizes. Against the standardized HQC scheme, while the public key is approximately twice as large, the ciphertext size is reduced by about 50%, offering superior storage efficiency in ciphertext-constrained environments.

Code-based group signatures are a promising candidate for post-quantum cryptography, but existing code-based group signature schemes struggle with the challenges of large signature sizes caused by zero-knowledge proofs. To address this issue, we propose a novel and practical code-based group signature scheme built upon the Schnorr-Lyubashevsky paradigm. Our construction achieves constant-size signatures and public keys, independent of the group cardinality, and its security is formally proven in the random oracle model under the hardness assumptions of the Syndrome Decoding (SD) and Decoding One Out of Many (DOOM) problems. To alleviate the performance bottleneck of rejection sampling, we design and implement a batch processing optimization for the signing algorithm, which significantly accelerates signature generation by applying vectorization to the most computationally intensive operations. Experimental results show that the optimization renders signing practical. Our scheme features the most compact signature size among existing codebased group signature schemes. All related code is open-sourced and available at https://github.com/Latters/CodeBasedGroupSig/.

Abstract In this paper, improved preimage attacks are presented on 3‐round Keccak‐256 and Keccak‐512 and 4‐round Keccak‐256 based on algebraic methods. The authors propose some new properties about the components of Keccak permutation, reconsider the existing preimage attacks, and further refine the linearisation processes of quadratic bits to lower the complexities. For 3‐round Keccak‐256 and Keccak‐512, priority is given to values with higher probability for quadratic bits, such that the guessing complexities decrease from slightly more than 2 65 and 2 440 to 2 64.79 and 2 424 , respectively. For preimage attack on 4‐round Keccak‐256, some strategies of saving degrees of freedom are applied to solve Boolean multivariate quadratic systems and reduce the guessing complexity from 2 196 to 2 188 .

In recent literature, a family of optimal linear locally recoverable codes (LRC codes) that attain the maximum possible distance (given code length, cardinality, and locality) is presented. The key ingredient for constructing such optimal linear LRC codes is the so-called r-good polynomials, where r is equal to the locality of the LRC code. However, given a prime p, known constructions of r-good polynomials over some extension field of Fp exist only for some special integers r, and the problem of constructing optimal LRC codes over small field for any given locality is still open. In this paper, by using function composition, we present two general methods of designing good polynomials, which lead to three new constructions of r-good polynomials. Such polynomials bring new constructions of optimal LRC codes. In particular, our constructed polynomials as well as the power functions yield optimal (n, k, r) LRC codes over Fq for all positive integers r as localities, where q is near the code length n.

Common substring problems allowing errors are known to be NP-hard. The main challenge of the problems lies in the combinatorial explosion of potential candidates. In this paper, we propose and study a generalized center string (GCS) problem, where not only all models (center strings) of any length, but also the positions of all their (degenerative) instances in input sequences are searched for. Inspired by frequent pattern mining techniques in data mining field, we present an exact and efficient method to solve GCS. First, a highly parallelized Trie-like structure, consensus tree, is proposed. Based on this structure, we present three Bpriori algorithms step by step. Bpriori algorithms can solve GCS with reasonable time and/or space complexities. We have proved that GCS is fixed parameter tractable with respect to fixed symbol set size and fixed length of input sequences. Experiment results on both artificial and real data have shown the correctness of the algorithms and the validity of our complexity analysis. A comparison with some current algorithms for solving common approximate substring problems is also given

Some properties of pn-periodic sequences over Fpwith fixed linear complexity value are found. Based on this, the distribution of the 1-error linear complexity of pn-periodic sequences over Fpis provided. The expectation of the 1-error linear complexity of random pn-periodic sequences over Fpis calculated and its estimated range is given. According to these results, an efficient algorithm for computing the 1-error linear complexity of a pn-periodic sequence, as well as a new algorithm for determining all the error vectors that give the 1-error linear complexity, is proposed

Correlation immune functions and resilient functions play important role in cryptography. The concept of correlation immune functions was first introduced and studied by Siegenthaler (1984). Correlation immune functions are used in stream ciphers as combining functions for running-key generators that are resistant to a correlation attack. We present a number of methods for constructing new resilient functions from old ones. These methods are significant generalizations of some previously known methods. The nonlinearity of some new constructed resilient functions is also discussed.