The Use of the Direct Sum Decomposition Algorithm for Analyzing the Strength of Some Mceliece Type Cryptosystems

Deundyak, V. M.; Kosolapov, Y. V.

doi:10.14529/mmp190308

Cited by 2 publications

(7 citation statements)

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“…In [13] it is shown that the analysis of McEliece-type system on the direct sum of codes can be reduced to the analysis of McEliece-type systems on the summands. In this paper, we have shown that the analysis of Sidel'nikov-type systems can also be reduced to the analysis of McEliece-type systems in some cases.…”

Section: Resultsmentioning

confidence: 99%

“…It is said that the code C is decomposable if this code is permutably equivalent to the direct sum of two or more nontrivial codes [21]. The code C is called a decomposable code with decomposition length u if it can be represented as the direct sum of u codes by the permutation of coordinates (see ( 10)) [13]. If in the decomposition (10) all codes C i are indecomposable, then such decomposition will be called complete.…”

Section: Decomposition Of Linear Codesmentioning

confidence: 99%

“…An algorithm for the code decomposition (see Algorithm 1) was constructed in [13]. Recall that c(∈ C) is minimal if there is no vector c linearly independent with c such that supp(c ) ⊆ supp(c) [23].…”

Section: Decomposition Of Linear Codesmentioning

confidence: 99%

“…The Decomposition algorithm is used in [13] for cryptanalysis the McEliecetype cryptosystem based on a direct sum of codes. The algorithm Decomposition can be modified to the algorithm DiagonalDecomposition with the same complexity.…”

Section: Lemmamentioning

confidence: 99%

“…Section 2 provides the necessary information about linear codes and merged codes. Section 3 provides an algorithm from [13] for decomposing a linear code into a direct sum of indecomposable subcodes. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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On the Decipherment of Sidel’nikov-Type Cryptosystems

Deundyak

Kosolapov

Maystrenko

2020

Code-Based Cryptography

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Asymmetric Sidel'nikov-type code-based cryptosystem is one of the generalizations of McEliece-type cryptosystems. The secret key in this generalization is the set of u randomly selected generator matrices GC 1 ,...,GC u of different [ni, k]-codes Ci, i ∈ {1, ..., u}. In addition, a part of the secret key is a random permutation ( u i=1 ni × u i=1 ni)-matrix P . The public key matrixG is the result of multiplying the concatenation of secret generator matrices and the matrix P :G = [GC 1 |...|GC u ]P . The security of these cryptosystems is based on the assumption that for u 2 it is computationally difficult to find inG such (k×ni)-submatrices composed of ni columns ofG, which would be generator matrices of codes permutably equivalent to the codes Ci, i = 1, ..., u. In the present paper, we construct an algorithm for the efficient search for such submatrices in the case when several conditions are satisfied. One of the conditions is the decomposability of the square of the connected codes C1,...,Cu into the direct sum of the squares of the codes Ci, i ∈ {1, ..., u}. An experimental assessment of the probability of fulfilling this condition for some Reed-Solomon codes, binary Reed-Muller codes, and Goppa code are also provided.

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Section: Resultsmentioning

confidence: 99%

Section: Decomposition Of Linear Codesmentioning

confidence: 99%

Section: Decomposition Of Linear Codesmentioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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