Improved cryptanalysis of rank metric schemes based on Gabidulin codes

Abstract

We prove that any variant of the GPT cryptosystem which uses a right column scrambler over the extension field as advocated by the works of Gabidulin et al. with the goal to resist to Overbeck's structural attack are actually still vulnerable to that attack. We show that by applying the Frobenius operator appropriately on the public key, it is possible to build a Gabidulin code having the same dimension as the original secret Gabidulin code but with a lower length. In particular, the code obtained by this way correct less errors than the secret one but its error correction capabilities are beyond the number of errors added by a sender, and consequently an attacker is able to decrypt any ciphertext with this degraded Gabidulin code. We also considered the case where an isometric transformation is applied in conjunction with a right column scrambler which has its entries in the extension field. We proved that this protection is useless both in terms of performance and security. Consequently, our results show that all the existing techniques aiming to hide the inherent algebraic structure of Gabidulin codes have failed.

An IND-CCA2 secure post-quantum encryption scheme and a secure cloud storage use case

“…According to the analysis in [18,[23][24][25], a secure code-based PKE scheme should be able to resist several structural attacks, such as key recovery attack, reduction attack and moore decomposition attack [23]. In particular, we can obtain the lower bound of the computation costs that an adversary needs to break a PKE scheme based on Gabidulin codes.…”

A New Rank Metric Codes Based Encryption Scheme

“…The reason is the inherent structure of the family of Gabidulin codes. A detailed analysis can be found in [Ksh07,OKN16]. We present the principle of the attacks.…”

“…From this date on, evolutions were proposed claiming to be secure against the existing attacks, [Gab08,GRH09,RGH10]. However, it was recently shown in [OKN16], that all existing variants could be reformulated as instances of the original problem, thus breakable in polynomial-time. Until now the common idea was that although rank metric would be a good candidate for designing code-based primitives with compact keys, a cryptosystem could not be designed from Gabidulin codes.…”

Geo Security using GPT Cryptosystem

“…To defend against these attacks several variants of GPT cryptosystems are proposed as well [12][13][14][15]. There were some recent attacks on the GPT cryptosystem published in [16][17][18] but to withstand these attack recently another construction of GPT cryptosystem is proposed by Loidreau P. [19]. Although GPT cryptosystem is continuously under threats over the years.…”