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The purpose of this paper is to demonstrate that a distinguisher of Reed-Solomon codes based on the square code construction leads to the cryptanalysis of several cryptosystems relying on them. These schemes are respectively (i) a homomorphic encryption scheme proposed by Bogdanov and Lee; (ii) a variation of the McEliece cryptosystem proposed by Baldi et… (More)

The Goppa Code Distinguishing (GD) problem consists in distinguishing the matrix of a Goppa code from a random matrix. The hardness of this problem is an assumption to prove the security of code-based cryptographic primitives such as McEliece's cryptosystem. Up to now, it is widely believed that the GD problem is a hard decision problem. We present the… (More)

The McEliece cryptosystem is a promising alternative to conventional public key encryption systems like RSA and ECC. In particular, it is supposed to resist even attackers equipped with quantum computers. Moreover, the encryption process requires only simple binary operations making it a good candidate for low cost devices like RFID tags. However,… (More)

Bogdanov and Lee suggested a homomorphic public-key encryption scheme based on error correcting codes. The underlying public code is a modified Reed-Solomon code obtained from inserting a zero submatrix in the Vandermonde generating matrix defining it. The columns that define this submatrix are kept secret and form a set L. We give here a distinguisher that… (More)

Baldi et 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… (More)

The BBCRS scheme is a variant of the McEliece public-key encryption scheme where the hiding phase is performed by taking the inverse of a matrix which is of the form T +R where T is a sparse matrix with average row/column weight equal to a very small quantity m, usually m < 2, and R is a matrix of small rank z 1. The rationale of this new transformation is… (More)

In the humid tropics, small ruminant farmers have to deal with gastrointestinal parasitic nematodes (GIN), among which anthelmintic resistant (AR) populations are rapidly spreading. Although targeted selective treatments (TSTs) are being increasingly used in breeding stock, suppressive drenchings remain the rule in younger animals, for safety and ease of… (More)

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