Scale, Round, Break: Simple Leakage Attacks on Secret Sharing Schemes

We study the local leakage resilience of $t$-out-of-$n$ threshold secret sharing schemes. We present a remarkably simple, perfectly correct attack that fully breaks any scheme with linear reconstruction over a finite field using $\lg t + \mathcal{O}(1)$ bits of leakage per share. In particular, this yields concretely efficient attacks on additive secret sharing and on Shamir’s scheme for arbitrarily large thresholds over arbitrarily large finite fields. Our key technical idea is an approximatel