International Association
for Cryptologic Research

Shamir's Secret Sharing Scheme allows for the distribution of information amongst n parties so that any t of them can combine their information to recover the secret. By design, it is secure against the total corruption of (t-1) parties, but open questions remain around its security against side-channel attacks, where an adversary may obtain a small amount of information about each of the n party's shares. An initial result by Benhamouda, Degwekar, Ishai and Rabin showed that if n is sufficiently large and t \geq 0.907n, then the scheme was secure under one bit of local leakage. These bounds continued to be improved in following works, and most recently Klein and Komargodski introduced a proof using a new analytical proxy that showed leakage resilience for t \geq 0.69n. In this paper we will use the analytic proxy of Klein and Komargodski to show leakage resilience for t \geq 0.668. We do this by introducing two new bounds on the proxy. The first uses a result from additive combinatorics to improve their original bound on the proxy. The second is an averaging argument that exploits the rarity of worst-case bounds occurring.