Breaking Multiplicative Knapsack Ciphers using a Genetic Algorithm IMAD F.T. YASEEN and H.V.SAHASRABUDDHE Dept. of computer science, University of Pune, Pune,India, 411 007. E-mail: {u96401, hvs}@cs.unipune.ernet.in Abstract In this paper we develop a genetic algorithm as a method for crypt- analysing multiplicative knapsack ciphers. Two new repair algorithms are presented in this work with the effect on the results. Our algorithm with the new techniques outperforms the previous results reported by Spillman [SPILLMAN,1993b] and by Kolodziejczyk [KOLODZIEJCZYK,1997]. The results show how the algorithm is effectively used to break knapsack ciphers by examining a very small fraction of the space of possible solutions. Un- like the ‘approximate’ answers found by some algorithms reported in the literature, our algorithm finds the exact solution in all cases. 1 Introduction Genetic Algorithms (GAs) have been applied successfully to many problems over the last 20 years, such as genetic synthesis, VLSI technology, strategy planning, machine learning, optimization problems, etc. In this paper we report applica- tion of a genetic algorithm to cryptography and specifically the cryptanalysis of knapsack ciphers. 2 Notation In the following, we have used capital letter variable names for vectors and small letter names for scalars. We shall use vector product notation, i.e AB = a 1 b 1 + a 2 b 2 + ... + a n b n . 1