Algebraic graphs and security of digital communications by Vasyl Ustimenko

By Vasyl Ustimenko

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Of course we can have some semantic similarity, between initial and encoded text. For instance, in the case of Galsworthy’s ”Forsythe Saga” the encoded text theoretically could be a translation of it into Spanish, but the probability of this happening is very small. 6. 1. e. the graph without cycles of length < g. In this case we will use a little bit different matching between arcs and strings of colors then in case of general regular graphs. Let w = Na (v) stands now for a neighbor of vertex v in graph Γ such that the color of the neighbor is a ∈ M .

Then pkey (Γ, n) = 1/(b(a − 1)[n/2] (b − 1)[n/2] ). Corollary 3. We are counting probabilities pmes and pkey in a equiprobable space. Thus the condition pmes = pkey corresponds to one time pad encryption scheme. Let (Γi , ni ) be a family of regular or bipartite biregular schemes of high girth with non decreasing ki and non decreasing bidegrees ai and bi such that ai + bi + ni is unbounded. Then (Γi , ni ) is a proper family of schemes. For instance, any sequence of schemes of high girth of unbounded degree or unbounded length of encoding arcs contains a subsequence of proper schemes.

Existence of free triangular optimal folders . . . . 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].

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