Download Algebraic graphs and security of digital communications by Vasyl Ustimenko PDF

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By Vasyl Ustimenko

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The algorithm of example 2 also can be implemented on Probabilistic Machine ( the result is the nearest to c ∈ Rn+1 vector from Z n+1 . One of the last results on Quantum Cryptography the reader can find in [1]. Remark. We can consider some union L of classes of watermarking equivalence and consider the restriction φn ′ of φn onto L. 4. Arithmetical dynamical systems on a free module and hidden discrete logarithm public key algorithms corresponding to φn ′ have been considered in [110]. In the section 6 we consider much more general encryption schemes in terms of special automata corresponding to families of directed algebraic graphs with special colouring.

4. Arithmetical dynamical systems on a free module and hidden discrete logarithm can be decrypted by the map Fa−1 written above. So the algorithm is symmetrical. The property 3 implies that different keys of length < cn produce distinct ciphertexts. We introduce the following directed graph φ = φ(n) corresponding to maps ft n and gt n over K n . Firstly we consider two copies of P (set of points) and L (set of lines) of the free module K n . We connect point p ∈ P with the line l ∈ L by directed arrow if and only if there is t ∈ Reg(K) such that ft (p) = l.

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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