2013
DOI: 10.1007/s11786-013-0163-8
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Improved Agreeing-Gluing Algorithm

Abstract: Abstract. In this paper we study the asymptotical complexity of solving a system of sparse algebraic equations over finite fields. An equation is called sparse if it depends on a bounded number of variables. Finding efficiently solutions to the system of such equations is an underlying hard problem in the cryptanalysis of modern ciphers. New deterministic Improved Agreeing-Gluing Algorithm is introduced. The expected running time of the Algorithm on uniformly random instances of the problem is rigorously estim… Show more

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Cited by 8 publications
(10 citation statements)
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“…Each MRHS equation corresponds to a system of multivariate polynomial equations. There are various methods proposed for solving general MRHS systems based on Gluing [3], [6], [7] or transformation to another type of problem [11], [13]. All of them have a worst-case exponential complexity.…”
Section: Pavol Zajacmentioning
confidence: 99%
“…Each MRHS equation corresponds to a system of multivariate polynomial equations. There are various methods proposed for solving general MRHS systems based on Gluing [3], [6], [7] or transformation to another type of problem [11], [13]. All of them have a worst-case exponential complexity.…”
Section: Pavol Zajacmentioning
confidence: 99%
“…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). Local reduction algorithms can also be combined with gluing [16], or used with recursive guessing and backtracking to provide an algorithm for solving a system similar to the DPLL algorithm used in SAT solvers [1]. The set S contains all possible right-hand sides.…”
Section: Gluing and Local Reductionmentioning
confidence: 99%
“…The main methods used to solve systems of MRHS equations are "gluing" and "agreeing" [13,14,16], and various versions of "local reduction" [1, 18,21]. Gluing relies on combining equations.…”
Section: Introductionmentioning
confidence: 99%
“…An effective algorithm to compute this intersection is Gluing [17], [18]. Complexity estimates for an improved version of Gluing on random equation systems are presented in [19].…”
Section: Preliminariesmentioning
confidence: 99%
“…The theoretical complexity bounds (e.g., [19]) are usually based on random equation system models, not on a concrete ciphers or families of ciphers. On the other hand, the experimental results (mostly based on SAT solvers) are restricted to smaller instances, and are often hard to scale to larger systems.…”
Section: Introductionmentioning
confidence: 99%