Algebraic Cryptanalysis of Present Based on the Method of Syllogisms

Lacko-Bartošová, Lucia

doi:10.2478/v10127-012-0047-3

Cited by 4 publications

(2 citation statements)

References 10 publications

(17 reference statements)

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“…This lemma is the basis of local reduction algorithms such as agreeing [13] and the method of syllogisms [3,[18][19][20], which use specific knowledge derived from the system to evaluate condition x 2 Sol.M/ ) M j x ¤ v even without knowing the solution set. By repeated applications the local reduction algorithms can be used to simplify the MRHS system and allow us, when it is computationally feasible, to find the solution set of the system (usually when there is exactly one or no solution).…”

Section: Gluing and Local Reductionmentioning

confidence: 99%

A new method to solve MRHS equation systems and its connection to group factorization

Zajac¹

2013

Journal of Mathematical Cryptology

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Multiple right-hand side (MRHS) equations over finite fields are a relatively new tool useful for algebraic cryptanalysis. The main advantage is in an efficient representation of the cryptographic primitives. The main methods to solve systems of MRHS equations are gluing, that relies on merging equations, and various versions of local reduction, that relies on removing partial solutions. In this paper we present a new algorithm to solve MRHS systems. The core of the algorithm is a transformation of the problem of solving an MRHS equation system into a problem of group factorization. We then provide two alternative algorithms to solve the transformed problem. One of these algorithms provides a further transformation to the well-studied closest vector problem. A corollary of our research is that the solution of the group factorization problem arising during the process of solving an MRHS equation system must be as difficult as the cryptanalysis of a corresponding block cipher described by this MRHS system.

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Section: Gluing and Local Reductionmentioning

confidence: 99%