Fuzzy Commitment Scheme based on Reed Solomon Codes

A Distinguisher-Based Attack on a Variant of McEliece's Cryptosystem Based on Reed-Solomon Codes

Baldi et \textit{al.} proposed a variant of McEliece's cryptosystem. The main idea is to replace its permutation matrix by adding to it a rank 1 matrix. The motivation for this change is twofold: it would allow the use of codes that were shown to be insecure in the original McEliece's cryptosystem, and it would reduce the key size while keeping the same security against generic decoding attacks. The authors suggest to use generalized Reed-Solomon codes instead of Goppa codes. The public code built with this method is not anymore a generalized Reed-Solomon code. On the other hand, it contains a…

Using Reed-Solomon codes in the $\left( U\mid U+V\right)$ construction and an application to cryptography

In this paper we present a modification of Reed-Solomon codes that beats the Guruwami-Sudan $1-\sqrt{R}$ decoding radius of Reed-Solomon codes at low rates $R$. The idea is to choose Reed-Solomon codes $U$ and $V$ with appropriate rates in a $\left( U\mid U+V\right)$ construction and to decode them with the Koetter-Vardy soft information decoder. We suggest to use a slightly more general version of these codes (but which has the same decoding performances as the $\left( U\mid U+V\right)$-construction) for code-based cryptography, namely to build a McEliece scheme. The point is here that these …

二维码与 Reed-Solomon 码的可靠性

Reliability on QR codes and Reed-Solomon codes

研究探讨了在 QR codes 中应用 Reed-Solomon 纠错码以提升抗故障能力，分析了其理论基础与 QR codes 结构，并揭示了利用纠错机制对模块进行选择性篡改的固有漏洞。

Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.

Encryption Scheme Based on Expanded Reed-Solomon Codes

We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes provides a safeguard against distinguisher attacks based on the Schur product. Moreover, without using a cyclic or a quasi-cyclic structure we obtain a key size reduction of nearly $45 \%$ compared to the classic McEliece cryptosystem proposed by Bernstein et al.

On the security of subspace subcodes of Reed-Solomon codes for public key encryption

This article discusses the security of McEliece-like encryption schemes using subspace subcodes of Reed-Solomon codes, i.e. subcodes of Reed-Solomon codes over $\mathbb{F}_{q^m}$ whose entries lie in a fixed collection of $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}$. These codes appear to be a natural generalisation of Goppa and alternant codes and provide a broader flexibility in designing code based encryption schemes. For the security analysis, we introduce a new operation on codes called the twisted product which yields a polynomial time distinguisher on such subspace subcodes as soon as…