Threshold Implementations in the Robust Probing Model

Abstract

Threshold Implementations (TI) are provably secure algorithmic countermeasures against side-channel attacks in the form of differential power analysis. The strength of TI lies in its minimal algorithmic requirements. These requirements have been studied over more than 10 years and many efficient implementations for symmetric primitives have been proposed. Thus, over the years the practice of protecting implementations matured, however, the theory behind threshold implementations remained the same. In this work, we revise this theory by looking at the properties of correctness, non-completeness, and uniformity as a composable security model. We prove that this model provides first-order and higherorder univariate security in the glitch-robust probing model which lets us expand the theoretic framework of TI. We first provide a link between uniformity and the notion of non-interference, a known composable security notion building out the probing model. We then relax the notion of non-completeness which helps the design of secure expansion and compression functions. Lastly, we provide generalisations of the threshold notions to allow for general secret sharing schemes and provide examples of how different sharing schemes affect the security and efficiency of the countermeasure.

Cryptanalysis of Masked Ciphers: A Not So Random Idea

“…The correctness property from Definition 4 is an absolute minimum requirement to obtain a meaningful implementation. Furthermore, if all layers of a threshold implementation are first-order non-complete and uniform, the resulting shared circuit can be proven secure in the first-order probing model considering glitches [21]. In the higher-order setting, the situation is more complicated.…”

“…To counter this, Nikova, Rechberger, and Rijmen [35] introduced the threshold implementation approach. From a formal point of view, the security of hardware-oriented countermeasures should be analyzed in a glitch-extended or robust probing model as formalized by Faust et al [23] and it can be shown that threshold implementations achieve such first-order robust probing security [21]. Unsurprisingly, achieving probing security often comes at a cost with respect to area usage, latency, energy consumption, and so on.…”

Guarding the First Order: The Rise of AES Maskings

“…Figure 3: Schematic illustration of a threshold implementation assuming an equal number of input and output shares [11].…”

Resilient uniformity: applying resiliency in masking

“…If all layers of a Threshold Implementation adhere to the above properties, the resulting shared circuit can be proven secure in the first-order probing model considering glitches, which is the security model defined further on [8]. In the higher-order setting, the situation is more complicated.…”