Stream Ciphers

Abstract

While Keeloq is an important cipher, used in industry and with an interesting set of methods for its cryptanalysis, the author believes that some more examples might be useful. Here, we present the ciphers Trivium and Bivium, as well as QUAD.

The purpose of this chapter is not only to exposit on how the ciphers presented here can be or cannot be attacked. Instead, the main purpose is to share some interesting ciphers and exposit on how those ciphers are converted into a system of equations. This relationship between the cipher and the equations is not trivial. The task of converting a cipher to equations, and doing so efficiently, is a major task in algebraic cryptanalysis. Also, because QUAD is based on random systems of equations, it is an endless source of cryptanalytic examples. The Bivium and Trivium equations are an excellent source for testing new techniques.

While great care has been taken to cite the work of others carefully, and note who has done what, the author wishes to be rather clear that nothing contained in this chapter whatsoever is his own idea, but rather taken from cited published papers, and presented in a more pedagogical style.