On the Power of Cascade Ciphers

Abstract

The unicity distance of a cascade of random. ciphers, w.r.t. known plaintext attack, is shown to be the sum of the key lengths. A time-space trade-off for the exhaustive cracking of a cascade of ciphers is shown. The structure of the set of permutations realized by a cascade is studied; it is shown that only l·2^k exhaustive experiments are necessary to determine the behavior of a cascade of l stages, each having k key bits. It is concluded that the cascade of random ciphers is not a random cipher. Yet, it is shown that, with high probability, the number of permutations realizable by a cascade of l random ciphers, each having k key bits, is 2^lk. Next, it is shown that two stages are not worse than one, by a simple reduction of the cracking problem of any of the stages to the cracking problem of the cascade. Finally, it is shown that proving a nonpolynomial lower bound on the cracking problem of long cascades is a hard task, since such a bound implies that P≠NP.

Part of this research was done while the author visited the Comp. Sci. Div. -EECS, Univ. of Cal., Berkeley. Supported by NSF grant No. MCS 82–04506 and the Fund for the Promotion of Research at the Technion.