Wednesday, August 17, 2011

Biclique Cryptanalysis of the Full AES

Since Rijndael was chosen as the Advanced Encryption Standard, improving upon 7-round attacks on the 128-bit key variant or upon 8-round attacks on the 192/256-bit key variants has been one of the most difficult challenges in the cryptanalysis of block ciphers for more than a decade. In this paper we present a novel technique of block cipher cryptanalysis with bicliques, which leads to the following results:
  • The first key recovery attack on the full AES-128 with computational complexity 2126.1.
  • The first key recovery attack on the full AES-192 with computational complexity 2189.7.
  • The first key recovery attack on the full AES-256 with computational complexity 2254.4.
  • Attacks with lower complexity on the reduced-round versions of AES not considered before, including an attack on 8-round AES-128 with complexity 2124.9.
  • Preimage attacks on compression functions based on the full AES versions.
In contrast to most shortcut attacks on AES variants, we do not need to assume any related-keys. Most of our attacks only need a very small part of the codebook and have small memory requirements, and are practically verified to a large extent. As our attacks are of high computational complexity, they do not threaten the practical use of AES in any way.

The biclique cryptanalysis successfully applies to all full versions of AES and compared to brute-force provides an advantage of about a factor 3 to 5, depending on the version. Also, it yields advantages of up to factor 15 for the key recovery of round-reduced AES variants with numbers of rounds higher than those cryptanalyed before.

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