Reducing a Masked Implementation’s Effective Security Order with Setup Manipulations

Couplings are a type of physical default that can violate the independence assumption needed for the secure implementation of the masking countermeasure. Two recent works by De Cnudde et al. put forward qualitatively that couplings can cause information leakages of lower order than theoretically expected. However, the (quantitative) amplitude of these lower-order leakages (e.g., measured as the amplitude of a detection metric such as Welch’s T statistic) was usually lower than the one of the (theoretically expected) dth order leakages. So the actual security level of these implementations remained unaffected. In addition, in order to make the couplings visible, the authors sometimes needed to amplify them internally (e.g., by tweaking the placement and routing or iterating linear operations on the shares). In this paper, we first show that the amplitude of low-order leakages in masked implementations can be amplified externally, by tweaking side-channel measurement setups in a way that is under control of a power analysis adversary. Our experiments put forward that the “effective security order” of both hardware (FPGA) and software (ARM-32) implementations can be reduced, leading to concrete reductions of their security level. For this purpose, we move from the detection-based analyzes of previous works to attack-based evaluations, allowing to confirm the exploitability of the lower-order leakages that we amplify. We also provide a tentative explanation for these effects based on couplings, and describe a model that can be used to predict them in function of the measurement setup’s external resistor and implementation’s supply voltage. We posit that the effective security orders observed are mainly due to “externally-amplified couplings” that can be systematically exploited by actual adversaries.

Glitch-Resistant Masking Revisited

Implementing the masking countermeasure in hardware is a delicate task. Various solutions have been proposed for this purpose over the last years: we focus on Threshold Implementations (TIs), Domain-Oriented Masking (DOM), the Unified Masking Approach (UMA) and Generic Low Latency Masking (GLM). The latter generally come with innovative ideas to cope with physical defaults such as glitches. Yet, and in contrast to the situation in software-oriented masking, these schemes have not been formally proven at arbitrary security orders and their composability properties were left unclear. So far, only a 2-cycle implementation of the seminal masking scheme by Ishai, Sahai and Wagner has been shown secure and composable in the robust probing model – a variation of the probing model aimed to capture physical defaults such as glitches – for any number of shares.In this paper, we argue that this lack of proofs for TIs, DOM, UMA and GLM makes the interpretation of their security guarantees difficult as the number of shares increases. For this purpose, we first put forward that the higher-order variants of all these schemes are affected by (local or composability) security flaws in the (robust) probing model, due to insufficient refreshing. We then show that composability and robustness against glitches cannot be analyzed independently. We finally detail how these abstract flaws translate into concrete (experimental) attacks, and discuss the additional constraints robust probing security implies on the need of registers. Despite not systematically leading to improved complexities at low security orders, e.g., with respect to the required number of measurements for a successful attack, we argue that these weaknesses provide a case for the need of security proofs in the robust probing model (or a similar abstraction) at higher security orders.