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Title:
Randomized Mixed-Radix Scalar Multiplication
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 \mathbb{N} satisfying the property that for every integer k in \mathbb{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 \mbox{n-covers}, we present a novel uniformly randomized scalar multiplication algorithm with built-in protections against various types of side-channel attacks. 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/2016/1022
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