In this paper, we deal with the problem of efficiently assessing the higher order vulnerability of a hardware cryptographic circuit. Our main concern is to provide methods that allow a circuit designer to detect early in the design cycle if the implementation of a Boolean-additive masking countermeasure does not hold up to the required protection order. To achieve this goal, we promote the search for vulnerabilities from a statistical problem to a purely symbolical one and then provide a method for reasoning about this new symbolical interpretation. Eventually we show, with a synthetic example, how the proposed conceptual tool can be used for exploring the vulnerability space of a cryptographic primitive

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This brief deals with the problem of mathematically formalizing hardware circuits' vulnerability to sidechannel attacks. We investigate whether spectral analysis is a useful analytical tool for this purpose by building a mathematically sound theory of the vulnerability phenomenon. This research was originally motivated by the need for deeper, more formal knowledge around vulnerable nonlinear circuits. However, while building this new theoretical framework, we discovered that it can consistently integrate known results about linear ones as well. Eventually, we found it adequate to formally model side-channel leakage in several significant scenarios. In particular, we have been able to find the vulnerability perimeter of a known cryptographic primitive (i.e., Keccak [1]) and thus tackle the analysis of vulnerability when signal glitches are present. We believe the conceptual framework we propose will be useful for researchers and practitioners in the field of applied cryptography and side-channel attacks.

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