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Title:
Randomizing scalar multiplication using exact covering systems of congruences
Authors: Eleonora Guerrini, Laurent Imbert, Théo Winterhalter
Abstract:A covering system of congruences can be defined as a set of congruence relations of the form: \{r_1 \pmod{m_1}, r_2 \pmod{m_2}, \dots, r_t \pmod{m_t}\} for m_1, \dots, m_t \in \N satisfying the property that for every integer k in \Z, there exists at least an index i \in \{1, \dots, t\} such that k \equiv r_i \pmod{m_i}. First, we show that most existing scalar multiplication algorithms can be formulated in terms of covering systems of congruences. Then, using a special form of covering systems called exact n-covers, we present a novel uniformly randomized scalar multiplication algorithm that may be used to counter differential side-channel attacks, and more generally physical attacks that require multiple executions of the algorithm. This algorithm can be an alternative to Coron’s scalar blinding technique for elliptic curves, in particular when the choice of a particular finite field tailored for speed compels to use a large random factor.
ePrint: https://eprint.iacr.org/2015/475
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