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A recent study suggests that arithmetic masking in prime fields leads to stronger security guarantees against passive physical adversaries than Boolean masking. Indeed, it is a common observation that the desired security amplification of Boolean masking collapses when the noise level in the measurements is too low. Arithmetic encodings in prime fields can help to maintain an exponential increase of the attack complexity in the number of shares even in such a challenging context. In this work, we contribute to this emerging topic in two main directions. First, we propose novel masked hardware gadgets for secure squaring in prime fields (since squaring is non-linear in non-binary fields) which prove to be significantly more resource-friendly than corresponding masked multiplications. We then formally show their local and compositional security for arbitrary orders. Second, we attempt to >experimentally evaluate the performance vs. security tradeoff of prime-field masking. In order to enable a first comparative case study in this regard, we exemplarily consider masked implementations of the AES as well as the recently proposed AESprime. AES-prime is a block cipher partially resembling the standard AES, but based on arithmetic operations modulo a small Mersenne prime. We present cost and performance figures for masked AES and AES-prime implementations, and experimentally evaluate their susceptibility to low-noise side-channel attacks. We consider both the dynamic and the static power consumption for our low-noise analyses and emulate strong adversaries. Static power attacks are indeed known as a threat for side-channel countermeasures that require a certain noise level to be effective because of the adversary’s ability to reduce the noise through intra-trace averaging. Our results show consistently that for the noise levels in our practical experiments, the masked prime-field implementations provide much higher security for the same number of shares. This compensates for the overheads prime computations lead to and remains true even if / despite leaking each share with a similar Signal-to-Noise Ratio (SNR) as their binary equivalents. We hope our results open the way towards new cipher designs tailored to best exploit the advantages of prime-field masking.

We describe how Pearson’s χ2-test can be used as a natural complement to Welch’s t-test for black box leakage detection. In particular, we show that by using these two tests in combination, we can mitigate some of the limitations due to the moment-based nature of existing detection techniques based on Welch’s t-test (e.g., for the evaluation of higher-order masked implementations with insufficient noise). We also show that Pearson’s χ2-test is naturally suited to analyze threshold implementations with information lying in multiple statistical moments, and can be easily extended to a distinguisher for key recovery attacks. As a result, we believe the proposed test and methodology are interesting complementary ingredients of the side-channel evaluation toolbox, for black box leakage detection and non-profiled attacks, and as a preliminary before more demanding advanced analyses., IACR Transactions on Cryptographic Hardware and Embedded Systems, Volume 2018, Issue 1