International Association
for Cryptologic Research

Leakage-resilient secret sharing schemes are a fundamental building block for secure computation in the presence of leakage. As a result, there is a strong interest in building secret sharing schemes that combine resilience in practical leakage scenarios with potential for efficient computation. In this work, we revisit the inner-product framework, where a secret $y$ is encoded by two vectors $(\omega, y)$, such that their inner product is equal to $y$. So far, the most efficient inner-product masking schemes (in which $\omega$ is public but random) are provably secure with the same security notions (e.g., in the abstract probing model) as additive, Boolean masking, yet at the cost of a slightly more expensive implementation. Hence, their advantage in terms of theoretical security guarantees remains unclear, also raising doubts about their practical relevance. We address this question by showing the leakage resilience of inner-product masking schemes, in the bounded leakage threat model. It depicts well implementation contexts where the physical noise is negligible. In this threat model, we show that if $m$ bits are leaked from the $d$ shares $y$ of the encoding over an $n$-bit field, then with probability at least $1−2^{-\lambda}$ over the choice of $\omega$, the scheme is $O(\sqrt{ 2^{−(d−1)·n+m+2\lambda}})$-leakage resilient. Furthermore, this result holds without assuming independent leakage from the shares, which may be challenging to enforce in practice. We additionally show that in large Mersenne-prime fields, a wise choice of the public coefficients $\omega$ can yield leakage resilience up to $O(n · 2^{−d·n+n+d})$, in the case where one physical bit from each share is revealed to the adversary. The exponential rate of the leakage resilience we put forward significantly improves upon previous bounds in additive masking, where the past literature exhibited a constant exponential rate only.