Automatic Search For Impossible Differentials Of SPECK With STP

SPECK is a family of lightweight and software-optimized block cipher,which proposed by the NSA in 2013 with the ARX designed strategy.There are only three basic operations in SPECK's round function:addition modulo 2n,bit rotation and XOR.In this paper,we review the definition,property and computation algo-rithm of the differential probability of modulo addition operation,and pro-pose a STP-based method for automatic search for impossible differentials of SPECK family.In the method,using Mouha's framework for finding differential characteristics of ARX cipher,we construct a STP model of impossible differ-entials for SPECK family,in which we describe the basic addition modulo 2n,bit rotation and XOR with a set of equations.We then can find impossible differentials through solving these equations with a STP constraint solver.We apply the method to SPECK family for finding impossible differen-tials with respect to the cased that the hamming weights of both input and output differences are exactly one.We find 6,6,6,7 and 7 rounds impossible differential of SPECK32,SPECK48,SPECK64,SPECK96 and SPECK128 re-spectively,with the corresponding number of the impossible differentials are 3,20,157,12,160.Furthermore,there are no longer rounds impossible differ-entials of SPECK family.