Algebraic Attack And Its Application

Recently, a new technique for cryptanalysis, algebraic attack, received a general concern by cryptographists. In this paper, we show the main theory of algebraic attack and its applications both incryptography and cryptanalysis. In the first chapter, we show how the algebraic attack has been proposed and its developments and status quo. In the second chapter, we introduce in brief the theory about algebraic geometry. In the third chapter, we illustrate the XL algorithm, an important algorithm used in algebraic attacks, and it applications in stream cipher. In the forth chapter, we illustrate the triangular list technique include the groebner base method and wu's method. In the last chapter, we introduce the trivium cryptosystem, a submission for the European project eSTREAM. Then we give a cryptanalysis for Trivium with algebraic attack.