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Solving multivariate polynomial systems and an invariant from commutative algebra. (arXiv:1706.06319v7 [cs.CR] UPDATED)
Sept. 22, 2022, 1:20 a.m. | Alessio Caminata, Elisa Gorla
cs.CR updates on arXiv.org arxiv.org
The complexity of computing the solutions of a system of multivariate
polynomial equations by means of Groebner bases computations is upper bounded
by a function of the solving degree. In this paper, we discuss how to
rigorously estimate the solving degree of a system, focusing on systems arising
within public-key cryptography. In particular, we show that it is upper bounded
by, and often equal to, the Castelnuovo-Mumford regularity of the ideal
generated by the homogenization of the equations of the …
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