On fibonacci keystream generators

Abstract

A number of keystream generators have been proposed which are based on Fibonacci sequences, and at least one has been fielded. They are attractive in that they can use some of the security results from the theory of shift register based keystream generators, while running much more quickly in software. However, new designs bring new risks, and we show how a system proposed at last year’s workshop, the Fibonacci Shrinking Genertor (FISH), can be broken by an opponent who knows a few thousand words of keystream. We then discuss how such attacks can be avoided, and present a new algorithm, PIKE, which is based on the A5 algorithm used in GSM telephones.