The Science of Guessing in Collision-Optimized Divide-and-Conquer Attacks

Recovering keys ranked in very deep candidate space efficiently is a very important but challenging issue in side-channel attacks (SCAs). State-of-the-art collision-optimized divide-and-conquer attacks (CODCAs) extract collision information from a collision attack to optimize the key recovery of a divide-and-conquer attack, and transform the very huge guessing space to a much smaller collision space. However, the inefficient collision detection makes them time consuming. The very limited collisions exploited and large performance difference between the collision attack and the divide-and-conquer attack in CODCAs also prevent their application in much larger spaces. In this article, we propose a Minkowski distance enhanced collision attack (MDCA) with performance closer to template attack (TA) compared to traditional correlation-enhanced collision attack (CECA), thus making the optimization more practical and meaningful. Next, we build a more advanced CODCA named full-collision chain (FCC) from TA and MDCA to exploit all collisions. Moreover, to minimize the thresholds while guaranteeing a high success probability of key recovery, we propose a fault-tolerant scheme to optimize FCC. The full key is divided into several big "blocks," on which a fault-tolerant vector (FTV) is exploited to flexibly adjust its chain space. Finally, guessing theory is exploited to optimize thresholds determination and search order of subkeys. Experimental results show that FCC notably outperforms the existing CODCAs.