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A new algorithms for computing discrete logarithms on elliptic curves defined over finite
fields is suggested. It is based on a new method to find zeroes of summation polynomials. In …

In this work, we propose a new way to (non-interactively, verifiably) demonstrate Quantum
Advantage by solving the average-case $\mathsf {NP} $ search problem of finding a solution …

In this work we analyze the security of cubic cryptographic constructions with respect to rank
weakness. We detail how to extend the big field idea from quadratic to cubic, and show that …

Semi-regular sequences over F 2 are sequences of homogeneous elements of the algebra
B (n)= F 2 [X 1,..., X n]/(X 1 2,..., X n 2), which have as few relations between them as …

In cryptography, by attacks reducing a cryptosystem to the problem that solves the system of
polynomial equations, several cryptosystems have been broken. The efficiency of an …

The best way of selecting samples in algebraic attacks against block ciphers is not well
explored and understood. We introduce a simple strategy for selecting the plaintexts and …

The first fall degree assumption provides a complexity approximation of Gröbner basis
algorithms when the degree of regularity of a polynomial system cannot be precisely …

Public key cryptosystems based on multivariate polynomials have been studied since the
eighties. One of them, called C∗, was introduced in 1988 by Imai and Matsumoto, and …

The Hidden Field Equation cryptosystem (HFE) is a public key encryption scheme whose
security relies on the hardness of solving a system of polynomial equations over the finite …