Extending Coggia–Couvreur attack on Loidreau’s rank-metric cryptosystem

Ghatak, Anirban

doi:10.1007/s10623-021-00972-7

Cited by 9 publications

(3 citation statements)

References 14 publications

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“…Furthermore, a straightforward verification shows that one can decrypt any ciphertext in polynomial time with the knowledge of G ′ and M ′ . This suggests that the cryptosystem degenerates into a sub-instance of Loidreau's proposal [4], which has been completely broken in some cases [29][30][31]. Hence choosing φ to be fully linear over F q n may bring some security problems.…”

Section: On the Choice Of φmentioning

confidence: 99%

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Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography

Guo

2022

Preprint

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This paper presents a new technique for disturbing the algebraic structure of linear codes in code-based cryptography. Specifically, we introduce the so-called semilinear transformations in coding theory and then apply them to the construction of code-based cryptosystems. Note that Fqm can be viewed as an Fq -linear space of dimension m , a semilinear transformation φ is therefore defined as an Fq -linear automorphism of Fqm . Then we impose this transformation to a linear code C over Fqm . It is clear that φ (C) forms an Fq -linear space, but generally does not preserve the Fqm -linearity any longer. Inspired by this observation, a new technique for masking the structure of linear codes is developed in this paper. Meanwhile, we endow the underlying Gabidulin code with the so-called partial cyclic structure to reduce the public-key size. Compared to some other code-based cryptosystems, our proposal admits a much more compact representation of public keys. For instance, 2592 bytes are enough to achieve the security of 256 bits, almost 403 times smaller than that of Classic McEliece entering the third round of the NIST PQC project.

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Section: On the Choice Of φmentioning

confidence: 99%

“…Not long after Coggia and Couvreur's work, this attack was generalized to the case of λ = 3 by Ghatak [30] and then by Duc and Loidreau [31].…”

Section: Structural Attacksmentioning

confidence: 99%

Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography

Guo

2022

Preprint

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“…In their cryptosystem, the published information consists of a generator matrix of the disturbed Gabidulin code by a random code that admits maximum rank weight n and a random vector of column rank n. This technique of masking the structure of Gabidulin codes, as claimed by Lau and Tan, can prevent some existing attacks [9][10][11][12]. Additionally, the recent Coggia-Couvreur attack [13] and Ghatak's attack [15] do not work on this cryptosystem either.…”

Section: Introductionmentioning

confidence: 99%

Polynomial-Time Key Recovery Attack on the Lau-Tan Cryptosystem Based on Gabidulin Codes

Guo¹,

Fu²

2021

Preprint

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This paper presents a key recovery attack on the cryptosystem proposed by Lau and Tan in a talk at ACISP 2018. The Lau-Tan cryptosystem uses Gabidulin codes as the underlying decodable code. To hide the algebraic structure of Gabidulin codes, the authors chose a matrix of column rank n to mix with a generator matrix of the secret Gabidulin code. The other part of the public key, however, reveals crucial information about the private key. Our analysis shows that the problem of recovering the private key can be reduced to solving a multivariate linear system over the base field, rather than solving a multivariate quadratic system as claimed by the authors. Solving the linear system for any nonzero solution permits us to recover the private key. Apparently, this attack costs polynomial time, and therefore completely breaks the cryptosystem.

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Cryptanalysis and Repair of a Gabidulin Code Based Cryptosystem from ACISP 2018

Guo

Fu²

2022

Information Security and Privacy

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Extending Coggia–Couvreur attack on Loidreau’s rank-metric cryptosystem

Cited by 9 publications

References 14 publications

Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography

Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography

Polynomial-Time Key Recovery Attack on the Lau-Tan Cryptosystem Based on Gabidulin Codes

Cryptanalysis and Repair of a Gabidulin Code Based Cryptosystem from ACISP 2018

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