Cryptology ePrint Archive: Report 2009/412

Distinguishing Attacks on Stream Ciphers Based on Arrays of Pseudo-random Words

Nathan Keller and Stephen D. Miller

Abstract: In numerous modern stream ciphers, the internal state consists of a large array of pseudo-random words, and the output key-stream is a relatively simple function of the state. In [Paul-Preneel], it was heuristically shown that in various cases this structure may lead to distinguishing attacks on the cipher. In this paper we further investigate this structural attack. We present a rigorous proof of the main probabilistic claim used in the attack in the basic cases, and demonstrate by examining a concrete example (the cipher SN3) that the heuristic assumptions of the attack are remarkably precise in more complicated cases. Furthermore, we use the general technique to devise a distinguishing attack on the stream cipher MV3 requiring $2^{82}$ words of key-stream. Unlike the attacks in [Paul-Preneel], our attack does not concentrate on the least significant bits of the words, thus allowing to handle the combination of more operations (XORs, modular additions and multiplications, and rotations by a fixed number of bits) in the update and output rules of the cipher.

Category / Keywords: public-key cryptography / stream ciphers, cryptanalysis

Date: received 25 Aug 2009

Contact author: miller at math rutgers edu

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Version: 20090901:065401 (All versions of this report)

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