Paper 2009/374

Key Recovery Attacks of Practical Complexity on AES Variants With Up To 10 Rounds

Alex Biryukov, Orr Dunkelman, Nathan Keller, Dmitry Khovratovich, and Adi Shamir

Abstract

AES is the best known and most widely used block cipher. Its three versions (AES-128, AES-192, and AES-256) differ in their key sizes (128 bits, 192 bits and 256 bits) and in their number of rounds (10, 12, and 14, respectively). In the case of AES-128, there is no known attack which is faster than the $2^{128}$ complexity of exhaustive search. However, AES-192 and AES-256 were recently shown to be breakable by attacks which require $2^{176}$ and $2^{119}$ time, respectively. While these complexities are much faster than exhaustive search, they are completely non-practical, and do not seem to pose any real threat to the security of AES-based systems. In this paper we describe several attacks which can break {\it with practical complexity} variants of AES-256 whose number of rounds are comparable to that of AES-128. One of our attacks uses only two related keys and $2^{39}$ time to recover the complete 256-bit key of a 9-round version of AES-256 (the best previous attack on this variant required 4 related keys and $2^{120}$ time). Another attack can break a 10 round version of AES-256 in $2^{45}$ time, but it uses a stronger type of {\it related subkey attack} (the best previous attack on this variant required 64 related keys and $2^{172}$ time). While neither AES-128 nor AES-256 can be directly broken by these attacks, the fact that their hybrid (which combines the smaller number of rounds from AES-128 along with the larger key size from AES-256) can be broken with such a low complexity raises serious concern about the remaining safety margin offered by the AES family of cryptosystems.