MAK Crypto Seminar: Chen Yuan and Oriol Farras

Two talks in this session:

TALK #1:

By: Chen Yuan, CWI Amsterdam
Title: Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

Abstract: Robust secret sharing enables the reconstruction of a secret-shared message in the presence of up to t (out of n) incorrect shares. The most challenging case is when n = 2t + 1, which is the largest t for which the task is still possible, up to a small error probability and with some overhead in the share size. In this work,we propose a new robust secret sharing scheme that offers full security against a rushing adversary. We also answer the open question posed by Cevallos et al.(Eurocrypt 2012) who proposed a scheme with overhead of O(n+K) and asked whether the linear dependency on n was necessary or not.

This is a joint work with Serge Fehr.

TALK #2:

By: Oriol Farras, URV Tarragona
Title: Secret-Sharing Schemes for General Access Structures

Abstract: A secret-sharing scheme allows some authorized sets of parties to reconstruct a secret; the collection of authorized sets is called the access structure. For over 30 years, it was known that any (monotone) collection of authorized sets can be realized by a secret-sharing scheme whose shares are of size $2^{n−o(n)}$ and until recently no better scheme was known. In a recent breakthrough, Liu and Vaikuntanathan (STOC 2018) reduced the share size to $O(2^{0.994n})$. We improved the general construction, obtaining a share size $O(2^{0.892n})$. For the special case of linear secret-sharing schemes, we get an exponent of $0.942$ (compared to $0.999$ of Liu and Vaikuntanathan).

This result was included in the paper "Secret-Sharing Schemes for General and Uniform Access Structures", a joint work with Benny Applebaum, Amos Beimel, Oded Nir and Naty Peter presented in Eurocrypt 2019.