Walks on Algebraic Small World Graphs of Large Girth and New Secure Stream Ciphers

The paper is dedicated to computer evaluation of parameters of members of family \(A(n, F_q)\) , \(n\ge 2\) of small world algebraic graphs of large girth with well defined projective limit. We present the applications of these computations to the area of optimisation problems for algebraic graphs over various fields and Cryptography. We show the impact of high girth property of known family of graphs \(A(n, F_q)\) on properties of fast stream ciphers based on these graphs. Finally we modify these symmetric encryption algorithms to make them resistant to linearization attacks.