# Read e-book online Algebraic graphs and security of digital communications PDF

By Vasyl Ustimenko

ISBN-10: 8362773170

ISBN-13: 9788362773176

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Extra info for Algebraic graphs and security of digital communications

Sample text

Let us consider the following general idea of walks on graphs as coding tools. Let Γ be a simple graph and V (Γ) its set of vertices. Let us refer to the sequence ρ = (v1 , v2 , . . , vn ), where vi ∈ V (Γ) , vi = vi+2 , i = 1, . . , n − 2, and vi is adjacent to vi+1 , i = 1, . . , n − 1 and ρ(v1 ) = vn as the encoding sequence and the encoded vertex of v1 . We refer to (vn , vn−1 , . . , v1 ) as the decoding sequence for vn . Let us imagine that our message is the password to a computer account.

Parallelotopic graphs of large girth and asymmetric algorithms . . . . . . . . . . . . . 7. The jump to commutative rings, dynamical systems and fast implementations . . . . . . . . . 8. Statistics related to mixing properties . . . . . 24 27 32 34 36 40 42 48 24 2. 1. 1. Walks on simple graphs and cryptography A combinatorial method of encryption with a certain similarity to the classical scheme of linear coding has been suggested in [107]. The general idea is to treat vertices of a graph as messages and arcs of a certain length as encryption tools.

K − 1 and d0 is the colour of plaintext, you obtain the plaintext u. Here we use the fact that u and c are vertices from the same component of D(k, q). In the package CRYPTIM we use this scheme in case s = t, degFi ≤ 1, in particular, for the problem of digital signatures. Remark 1. The probability to have same invariants a2 , . . , at+1 for two random messages is about 1/q t . 41 42 2. Simple graphs with special arcs and Cryptography Remark 2. If we want to speed up the computation of c(u) we may present it to our correspondent as product of several factors.