Error Correcting Coding and Security for Data Networks

Kabatiansky, Grigory; Krouk, Evgenii; Semenov, Sergei

doi:10.1002/0470867574

Cited by 69 publications

(45 citation statements)

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“…If we want to avoid that the knowledge of a message/signature pair allows to recover the secret key, this implies for instance that the rate R of C known should be significantly larger than 2ρ, that is twice the rate of the secret code C hidden . This would change the parameters of the scheme significantly and give much larger key sizes than has been proposed in [KKS97, KKS05,BMJ11].…”

Section: Discussionmentioning

confidence: 99%

“…A possible approach to meet this goal could be to build such schemes whose security relies on the difficulty of decoding linear codes. Two code based schemes of this kind have been proposed, namely the Courtois-Finiasz-Sendrier signature scheme [CFS01] and the Kabatianskii, Krouk and Smeets (KKS) scheme [KKS97,KKS05].…”

Section: Introductionmentioning

confidence: 99%

“…It turns out that such algorithms are unusually successful in this setting due to the conjunction of three factors: (i) there are many low-weight codewords, (ii) they are localized on a rather small support, (iii) some part of this support is known to the attacker. It appears that all parameters suggested in [KKS97, KKS05,BMJ11] are easily broken by this approach and this without even knowing a single signature pair. Moreover, this approach can exploit the knowledge of a message-signature pair which speeds up the attack.…”

Section: Introductionmentioning

confidence: 99%

“…We provide an analysis of this attack which explains what makes it feasible for the parameters proposed in [KKS97, KKS05,BMJ11]. The KKS scheme relies on a couple of matrices which can be viewed as parity-check matrices of two linear codes.…”

Section: Introductionmentioning

confidence: 99%

“…This phenomenon was clearly not taken into in the parameters suggested in [KKS97, KKS05,BMJ11] as shown in Table 1. The values of d GV (|I |, k) are extremely low (in the range 1 − 6).…”

mentioning

confidence: 99%

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An Efficient Attack on All Concrete KKS Proposals

Otmani¹,

Tillich²

2011

Lecture Notes in Computer Science

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Abstract. Kabastianskii, Krouk and Smeets proposed in 1997 a digital signature scheme based on a couple of random error-correcting codes. A variation of this scheme was proposed recently and was proved to be EUF-1CMA secure in the random oracle model. In this paper we investigate the security of these schemes and suggest a simple attack based on (essentially) Stern's algorithm for finding low weight codewords. It efficiently recovers the private key of all schemes of this type existing in the literature. This is basically due to the fact that we can define a code from the available public data with unusual properties: it has many codewords whose support is concentrated in a rather small subset. In such a case, Stern's algorithm performs much better and we provide a theoretical analysis substantiating this claim. Our analysis actually shows that the insecurity of the proposed parameters is related to the fact that the rates of the couple of random codes used in the scheme were chosen to be too close. This does not compromise the security of the whole KKS scheme. It just points out that the region of weak parameters is really much larger than previously thought.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This phenomenon was clearly not taken into in the parameters suggested in [KKS97, KKS05,BMJ11] as shown in Table 1. The values of d GV (|I |, k) are extremely low (in the range 1 − 6).…”

mentioning

confidence: 99%

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