On the Comparison of Cryptographical Properties of Two Different Families of Graphs with Large Cycle Indicator

The paper is devoted to the implementations of the public key algorithms based on simple algebraic graphs A(n, K ) and D(n, K ) defined over the same finite commutative ring K . If K is a finite field both families are families of graphs with large cycle indicator. In fact, the family D(n, Fq) is a family of graphs of large girth (f.g.l.g.) with c = 1, their connected components C D(n, Fq) form the f.g.l.g. with the speed of growth 4/3. Family A(n, q), charFq = 2 is a family of connected graphs with large cycle indicator with the largest possible speed of growth. The computer simulation demonstrates the advantage (better density which is the number of monomial expressions) of public rules derived from A(n, q) in comparison with symbolic algorithm based on graphs D(n, q).