arXiv subjects

Abhinaba Mazumder

Publications and source records attributed to Abhinaba Mazumder.

5 recordsLinked to original sources

arXiv2026

Search-to-Decision Reductions for the Linear and General Code Equivalence Problems

In this paper, we present efficient search-to-decision reductions for the Linear Code Equivalence (LCE) and Generalised Code Equivalence (GCE) problems. Our methodology is inspired by the recent search-to-decision reduction for Permutation Code Equivalence. We demonstrate how to recover the permutation component of the equivalence using a decision oracle, and subsequently show one way of recovering the diagonal and field automorphism components in deterministic polynomial time by leveraging the elegant Engel-Schneider algorithm for diagonal equivalence.

cs.IT↗

arXiv2026

An Attack on High Rate McEliece Cryptosystems Using Generalized Reed Solomon Codes with Weight $2$ Mask

Due to the insecurity of McEliece cryptosystems instantiated with Generalized Reed-Solomon codes, there have been several proposals of McEliece type systems that replace the permutation matrix by a matrix $M$ with larger row and column weight. In many of them, the secret key is still a GRS code. There have been successful attacks on some of those schemes with row and column weight between $1$ and $1 + R$, where $R$ is the rate of the code. The case of weight two and larger has been left open in these works. Subsequently, several authors proposed schemes with weight exactly two and with even higher weight. We provide distinguishers for the public codes appearing in these cryptosystems in the high rate regime. In addition, we give a framework to turn a good enough distinguisher into a key-recovery attack. In the case where the matrix $M$ has row and column weight $2$, we can successfully attack the scheme in the high rate regime using a cube code distinguisher.

cs.CR↗

arXiv2026

A Survey on Code Equivalence: The State-of-the-Art and Open Questions

In this work, we provide a comprehensive survey of the code equivalence problem and its variants. We explain the existing results, highlighting the relationships between different problem formulations, algorithmic techniques, and hardness assumptions. In addition, we systematically review known attacks, identify the parameter regimes in which they are effective, and discuss their limitations. Lastly, we outline several open problems and research directions, with the aim of clarifying the current landscape and guiding future work toward a deeper understanding of the hardness of code equivalence.

cs.IT↗

arXiv2026

The Power of Power Codes: New Classes of Easy Instances for the Linear Equivalence Problem

Given two linear codes, the Linear Equivalence Problem (LEP) asks to find (if it exists) a linear isometry between them; as a special case, we have the Permutation Equivalence Problem (PEP), in which isometries must be permutations. LEP and PEP have recently gained renewed interest as the security foundations for several post-quantum schemes, including LESS. A recent paper has introduced the use of the Schur product to solve PEP, identifying many new easy-to-solve instances. In this paper, we extend this result to LEP. In particular, we generalize the approach and rely on the more general notion of power codes. Combining it with Frobenius automorphisms and Hermitian hulls, we identify many classes of easy LEP instances. To the best of our knowledge, this is the first work exploiting algebraic weaknesses for LEP. Finally we show an improved reduction to PEP whenever the coefficients of the monomial matrix are in a subgroup of the multiplicative group of the finite field.

cs.CR↗

arXiv2025

Information-Set Decoding for Convolutional Codes

In this paper, we present a framework for generic decoding of convolutional codes, which allows us to do cryptanalysis of code-based systems that use convolutional codes. We then apply this framework to information set decoding, study success probabilities and give tools to choose variables. Finally, we use this to attack two cryptosystems based on convolutional codes. In the first, our code recovered about 74% of errors in less than 10 hours each, and in the second case, we give experimental evidence that 80% of the errors can be recovered in times corresponding to about 70 bits of operational security, with some instances being significantly lower.

cs.IT↗