String Transformation Based On 3 -quasigroups

Edon80 is one of the eight hardware oriented stream ciphers, which is into the last round selection of the European e-STREAM planning, the core of which is based on the nonlinear operation of four quasigroups of order four and eighty nonlinear iteration. At present, the most effective attack is the key recovery attack [1] which was given by Hell and Johansson. The attack takes advantage of a shorter Edon80 key sequence cycle (cycle expectations about 2103) and only 2 and 3 as cycle length prime factors. However, if we use a 3-quasigroup replace the four quasigroups of order four in Edon80, and introduce the new string transform algorithm, then the mathematical expectation of the cycle length will increase to 2254, and the prime factors will be 2, 3,5,7,11,13. Therefore the key recovery attack of Hell and Johansson will be invalid in this situation. So, in this paper we will give a string transformation based on a combinatorial design called 3-quasigroups. A 3-quasigroup is equivalent to a Latin cube and one of its most important properties is that all possible element occurs with equal probability. This leads the uniform distribution of substrings of certain length in the resulting sequence get by a series transformations apply on an initial string. We can also choose proper 3-quasigroups to make that the period of the resulting string increases exponentially with the number of times the transformation applied. This string transformation we have defined will be useful in the design of pseudo-random sequence generators and in the research of stream ciphers.The whole paper is divided into four chapters.Chapter 1:In this chapter, above all, we introduce the backgrounds, develop-ments of stream cipher and pseudo random sequence, as well as the contact between them, then give the developments of the periods of the stream cipher Edon80, at last, we illustrate the main work of this article.Chapter 2:In this chapter, first of all, we give the definition of the string trans-formation based on a 3-quasigroup and prove some properties of the transformation, furthermore, we prove the uniformity of the substring distribution in the resulting string and last but not the least, we give a simulation of the the transformation to show the uniformity of the substring distribution.Chapter 3:In this chapter, we discuss the period distribution of the resulting strings.Chapter 4:In this chapter, we make summary of the work as well as the prospect of the work.