GE vs GM: Efficient side-channel security evaluations on full cryptographic keys

Abstract

Security evaluations for full cryptographic keys is a very important research topic since the past decade. An efficient rank estimation algorithm was proposed at FSE 2015 to approximate the empirical guessing entropy remaining after a side-channel attack on a full AES key, by combining information from attacks on each byte of he key independently. However, these could not easily scale to very large keys over 1024 bits. Hence, at CHES 2017, it was proposed a new approach for scalable security evaluations based on Massey’s guessing entropy, which was shown tight and scalable to very large keys, even beyond 8192 bits. Then, at CHES 2020, it was proposed a new method for estimating the empirical guessing entropy for the case of full-key evaluations, showing also important divergences between the empirical guessing entropy and Massey’s guessing entropy. However, there has been some confusion in recent publications of side-channel evaluation methods relying on these two variants of the guessing entropy. Furthermore, it remained an open problem to decide which of these methods should be used and in which context, particularly given the wide acceptance of the empirical guessing entropy in the side-channel community and the relatively little use of the other.
In this paper, we tackle this open problem through several contributions. First of all, we provide an unitary presentation of both versions of the guessing entropy, allowing an easy comparison of the two metrics. Secondly, we compare the two metrics using a set of common and relevant indicators, as well as three different datasets for side-channel evaluations (simulated, AVR XMEGA 8-bit microcontroller and a 32-bit device). We used these indicators and datasets also to compare the three full-key evaluation methods from FSE 2015, CHES 2017 and CHES 2020, allowing us to provide a clear overview of the usefulness and limitations of each method. Furthermore, our analysis has enabled us to find a new method for verifying the soundness of a leakage model, by comparing both versions of the guessing entropy. This method can be easily extended to full-key evaluations, hence leading to a new useful method for side-channel evaluations.