Cryptology ePrint Archive: Report 2010/248

Automatic Search for Related-Key Diff erential Characteristics in Byte-Oriented Block Ciphers: Application to AES, Camellia, Khazad and Others

Alex Biryukov and Ivica Nikolić

Abstract: While di fferential behavior of modern ciphers in a single secret key scenario is relatively well understood, and simple techniques for computation of security lower bounds are readily available, the security of modern block ciphers against related-key attacks is still very ad hoc. In this paper we make a first step towards provable security of block ciphers against related-key attacks by presenting an efficient search tool for finding diff erential characteristics both in the state and in the key (note that due to similarities between block ciphers and hash functions such tool will be useful in analysis of hash functions as well). We use this tool to search for the best possible (in terms of the number of rounds) related-key diff erential characteristics in AES, byte-Camellia, Khazad, FOX, and Anubis. We show the best related-key diff erential characteristics for 5, 11, and 14 rounds of AES-128, AES-192, and AES-256 respectively. We use the optimal diff erential characteristics to design the best related-key and chosen key attacks on AES-128 (7 out of 10 rounds), AES-192 (full 12 rounds), byte-Camellia (full 18 rounds) and Khazad (7 and 8 out of 8 rounds). We also show that ciphers FOX and Anubis have no related-key attacks on more than 4-5 rounds.

Category / Keywords: secret-key cryptography /

Date: received 30 Apr 2010

Contact author: ivica nikolic at uni lu

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Version: 20100502:170337 (All versions of this report)

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