Abstract

Algebraic graphs D(n, q) and their analog graphs D(n, K), where K is a finite commutative ring were used successfully in Coding Theory (as Tanner graphs for the construction of LDPC codes and turbo-codes) and in Cryptography (stream-ciphers, public-keys and tools for the key-exchange protocols. Many properties of cryptography algorithms largely depend on the choice of finite field Fq or commutative ring K. For practical implementations the most convenient fields are F and rings modulo Z modulo 2m. In this paper the reader can find the first results about the comparison of D(n, 2m) based stream-ciphers for m = 8, 16, 32 implemented in C++. They show that performance (speed) of algorithms gets better when m is increased.

Highlights

  • Algebraic graphs D(n, q) over finite fields Fq without cycles of length less than n + 5 have been introduced in [1]

  • In [5, 6] we presented some encryption tools based on walking on algebraic graphs over finite fields

  • We implemented a new variable unit size symmetric stream key dependent cipher based on the algebraic graph using the finite field

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Summary

Introduction

Algebraic graphs D(n, q) over finite fields Fq without cycles of length less than n + 5 have been introduced in [1]. It has been shown that the confusion properties of the algorithm get better when the graph based encryption map takes into account the combination of two special affine transformations of the cipher space. In [5, 6] we presented some encryption tools based on walking on algebraic graphs over finite fields. The connected components of graphs D(n, q) grow with the growth of n (as well as with the growth of q) It means that our algorithms are not unit ciphers see [9]. It is known that the proposed family of graphs has no cycle of length n + 5, for n > 3 where n is the length (number of bytes) of the plain text This property ensures that if the length of the password l < (n + 5)/2, each password will have a unique walk path.

Basic Definitions
Walk on Graph Algorithm
Conclusions
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