Improved Linear Analysis on Block Cipher MULTI2

Abstract

Developed by Hitachi, MULTI2 is a block cipher used mainly to secure the multimedia content. It was registered in ISO/IEC 9979 and was patented in US and Japan. MULTI2 uses the Feistel structure and operates on the 64-bit blocks. The encryption key has 256 bits.

This paper studies the linear analysis on MULTI2. We give a detailed bias analysis on MULTI2 round functions. For the first time formal proofs on their bias properties are given. This allows to find a new 4-round bias 2^− 2. Previously, the best 4-round bias 2^− 5.7 was proposed. Using our results on the MULTI2 round functions, we propose the linear attacks on r-round MUTLI2 to recover the encryption key. Our linear attack can recover the 256-bit encryption key in time 2⁴⁶, 2^60.4, 2^83.8, 2^91.7, 2^123.4, 2^123.2 of r-round encryptions for r = 8,12,16,20,24,28 respectively. Further, we can recover the 32-bit sub-key in last round much faster than the whole encryption key recovery, i.e., in time 2³⁷ for r = 8,12,16,20,24. Note that previously, the best linear key-recovery attack was a 20-round attack with time 2^93.4 (of 20-round encryptions) and data 2^39.2. As ISO register recommends to use at least 32 rounds, our attacks remain to be theoretical and do not threaten security for the practical use currently.

This work is supported by the National Science and Technology Major Project under Grant No. 2010ZX01036-001-002 & 2010ZX01037-001-002, the Knowledge Innovation Key Directional Program of Chinese Academy of Sciences under Grant No. KGCX2-YW-125 & KGCX2-YW-174, and the National Natural Science Foundation of China under Grant No. 61170072.