Paper 2009/405

Generic Attacks on Misty Schemes -5 rounds is not enough-

Valerie Nachef, Jacques Patarin, and Joana Treger

Abstract

Misty schemes are classic cryptographic schemes used to construct pseudo-random permutations from $2n$ bits to $2n$ bits by using $d$ pseudo-random permutations from $n$ bits to $n$ bits. These $d$ permutations will be called the ``internal'' permutations, and $d$ is the number of rounds of the Misty scheme. Misty schemes are important from a practical point of view since for example, the Kasumi algorithm based on Misty schemes has been adopted as the standard blockcipher in the third generation mobile systems. In this paper we describe the best known ``generic'' attacks on Misty schemes, i.e. attacks when the internal permutations do not have special properties, or are randomly chosen. We describe known plaintext attacks (KPA), non-adaptive chosen plaintext attacks (CPA-1) and adaptive chosen plaintext and ciphertext attacks (CPCA-2) against these schemes. Some of these attacks were previously known, some are new. One important result of this paper is that we will show that when $d=5$ rounds, there exist such attacks with a complexity strictly less than $2^{2n}$. Consequently, at least 6 rounds are necessary to avoid these generic attacks on Misty schemes. When $d \geq 6$ we also describe some attacks on Misty generators, i.e. attacks where more than one Misty permutation is required.