Welcome to the resource topic for 2022/1668
Title:
On the families of graphs with the fastest growth of girth and their usage in cryptography
Authors: Vasyl Ustimenko
Abstract:Symbolic computations with usage of algebraic graphs A(n; F_q)
and A(n;,F_q[x_1, x_2,…, x_n]) were used for the development of various
cryptographic algorithms because the length of their minimal cycle (the
girth) tends to infinity when n is growing. It was announced recently that
for each commutative integrity ring the girth of A(n, K) is ≥ 2n. In this
paper we present essentially shorter closed proof of this statement and
evaluate the girth of some induced subgraphs of A(n; K[x_1, x_2, …, x_n]).
ePrint: https://eprint.iacr.org/2022/1668
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