Enhancing side-channel analysis of binary-field multiplication with bit reliability

Abstract

At Africacrypt 2010, Medwed et al. presented Fresh Re-Keying as a countermeasure to protect low-cost devices against sidechannel analysis. They propose to use binary-field multiplication as a re-keying function. In this paper, we present a new side-channel attack on this construction (and multiplication in general). By using template attacks and the simple algebraic structure of multiplication, the problem of key recovery can be casted to the well known Learning Parity with Noise problem (LPN). However, instead of using standard LPN solving algorithms, we present a method which makes extensive use of bit reliabilities derived from side-channel information. It allows us to decrease the attack runtime in cases with low-to-medium error probabilities. In a practical experiment, we can successfully attack a protected 8-bit Fresh Re-Keying implementation by Medwed et al. using only 512 traces.