The Improved 96th-Order Differential Attack on 11 Rounds of the Block Cipher CLEFIA

Abstract

CLEFIA is a 128-bit block cipher proposed by Shirai of SONY et al. in 2007. Its key size is 128, 192, or 256 bits. The number of the round of data processing part depends on a key size, viz. it is 18, 22, or 26 rounds for 128, 192, or 256 bits of a key size, respectively. Such a characteristic of CLEFIA have been known that the 96th- order differential of 64 bits out of 128 bits of the 8th-round's output is zero. With this characteristic, we reported the 96th-order differential attack on 11 rounds of CLEFIA that requires 2 98.3 blocks of plain text and 2 159 times of data encryption. In this paper, we reduce this number of the times of the encryption, (viz. computational complexity) by applying a partial sum technique proposed by Ferguson et al. With the technique, we sequentially derive a modulo 2 occurrence distribution of intermediate data of cryptanalysis. We also reduce the complexity by introducing a nested structure of iterative computations to the attack algorithm. As a result we reduce the complexity to 2 106.6 , which is 1/2 52.4 of the conventional complexity. 