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Reconstructing points of superelliptic curves over a prime finite field

Abstract: Let p be a prime and Fp the finite field with p elements. We show how, when given an superelliptic curve Y n + f(X) ? Fp[X, Y ] and an approximation to (v0, v1) ? F2 p such that vn 1 = ?f(v0), one can recover (v0, v1) efficiently, if the approximation is good enough. As consequence we provide an upper bound on the number of roots of such bivariate polynomials where the roots have certain restrictions. The results has been motivated by the predictability problem for non-linear pseudorandom number generators and, other potential applications to cryptography.

 Authorship: Gutierrez J.,

 Fuente: Advances in Mathematics of Communications, 2024, 18(1), 222-232

 Publisher: American Institute of Mathematical Sciences

 Year of publication: 2024

 No. of pages: 11

 Publication type: Article

 DOI: 10.3934/amc.2022022

 ISSN: 1930-5346,1930-5338

 Spanish project: PID2019-110633GB-I00