Pseudo-Linear Approximations for ARX Ciphers: With Application to Threefish.
Kerry A. McKay, Poorvi L. Vora · IACR Cryptology ePrint Archive · 2010
The operations addition modulo 2 and exclusive-or have recently been combined to obtain an efficient mechanism for nonlinearity in block cipher design. In this paper, we show that ciphers using this approach may be approximated by pseudo-linear expressions relating groups of contiguous bits of the round key, round input, and round output. The bias of an approximation can be large enough for known plaintext attacks. We demonstrate an application of this concept to a reduced-round version of the Threefish block cipher, a component of the Skein entry in the secure hash function competition.