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Algebraic attacks using SAT-solvers. (English) Zbl 1213.13043
An algebraic attack on a cryptosystem consists of transforming the problem into the solution of a system of polynomial equations, usually over a finite field. The paper “Algebraic attacks using SAT-solvers” discusses different ways to efficiently transform the polynomial system into a logical clause. These CNF-clauses are then attackable using SAT-solvers. The authors also consider the sub-problem of efficiently reducing systems in fields of size a power of two to the Boolean field. The paper shows experimentally that using SAT-solvers to attack cryptosystems is feasible. It outperforms Gröbner basis methods by orders of magnitude.

MSC:
13P15 Solving polynomial systems; resultants
03B35 Mechanization of proofs and logical operations
68W30 Symbolic computation and algebraic computation
94A60 Cryptography
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References:
[1] Courtois N., LNCS 4887 pp 152– (2007)
[2] Massacci F., J. Automated Reasoning 24 pp 165– (2000) · Zbl 0968.68052
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