A distinguisher on PRESENT-like permutations with application to SPONGENT

Abstract

At Crypto 2015, Blondeau et al. showed a known-key analysis on the full PRESENT lightweight block cipher. Based on some of the best differential distinguishers, they introduced a meet in the middle (MitM) layer to pre-add the differential distinguisher, which extends the number of attacked rounds on PRESENT from 26 rounds to full rounds without reducing differential probability. In this paper, we generalize their method and present a distinguisher on a kind of permutations called PRESENT-like permutations. This generic distinguisher is divided into two phases. The first phase is a truncated differential distinguisher with strong bias, which describes the unbalance of the output collision on some fixed bits, given the fixed input in some bits, and we take advantage of the strong relation between truncated differential probability and capacity of multidimensional linear approximation to derive the best differential distinguishers. The second phase is the meet-in-the-middle layer, which is pre-added to the truncated differential to propagate the differential properties as far as possible. Different with Blondeau et al.’s work, we extend the MitM layers on a 64-bit internal state to states with any size, and we also give a concrete bound to estimate the attacked rounds of the MitM layer. As an illustration, we apply our technique to all versions of SPONGENT permutations. In the truncated differential phase, as a result we reach one, two or three rounds more than the results shown by the designers. In the meet-in-the-middle phase, we get up to 11 rounds to pre-add to the differential distinguishers. Totally, we improve the previous distinguishers on all versions of SPONGENT permutations by up to 13 rounds.

创新点

我们推广了Blondeau等人在2015年美密会上对轻量级密码算法PRESENT的分析方法, 给出PRESENT类置换的区分器。我们的区分器包含两层: 截断差分层和中间相遇层。在截断差分层, 我们利用线性近似与截断差分之间的关系找到寻找具有强偏差的差分区分器的一般方法; 在中间相遇层, 我们扩展了Blondeau等人的结果得到能够处理任意中间状态的一般方法, 并对中间相遇层实现的轮数给出估计。然后用我们的一般方法分析了SPONGENT的13个版本: 在截断差分层, 要比设计者估计的轮数多两到三轮; 在中间相遇层, 我们得到了高达11轮的结果, 所以在SPONGENT的所有版本的分析中, 比以前的分析结果多出最多13轮。