Paper 2018/869

Higher-Order DCA against Standard Side-Channel Countermeasures

Andrey Bogdanov and Matthieu Rivain and Philip S. Vejre and Junwei Wang

Abstract

At CHES 2016, Bos et al. introduced $\textit{differential computational analysis}$ (DCA) as an attack on white-box software implementations of block ciphers. This attack builds on the same principles as DPA in the classical side-channel context, but uses computational traces consisting of plain values computed by the implementation during execution. This attack was shown to be able to recover the key of many existing AES white-box implementations. The DCA adversary is $\textit{passive}$, and so does not exploit the full power of the white-box setting, implying that many white-box schemes are insecure even in a weaker setting than the one they were designed for. It is therefore important to develop implementations which are resistant to this attack. We investigate the approach of applying standard side-channel countermeasures such as $\textit{masking}$ and $\textit{shuffling}$. Under some necessary conditions on the underlying randomness generation, we show that these countermeasures provide resistance to standard (first-order) DCA. Furthermore, we introduce $\textit{higher-order DCA}$, along with an enhanced $\textit{multivariate}$ version, and analyze the security of the countermeasures against these attacks. We derive analytic expressions for the complexity of the attacks -- backed up through extensive attack experiments -- enabling a designer to quantify the security level of a masked and shuffled implementation in the (higher-order) DCA setting.