TY - GEN

T1 - Better secret sharing via robust conditional disclosure of secrets

AU - Applebaum, Benny

AU - Beimel, Amos

AU - Nir, Oded

AU - Peter, Naty

N1 - Funding Information:
The first and third authors are supported by the European Union’s Horizon 2020 Programme (ERC-StG-2014-2020) under grant agreement no. 639813 ERC-CLC, and the Check Point Institute for Information Security. This work was done while the second author was visiting Georgetown University, supported by NSF grant no. 1565387, TWC: Large: Collaborative: Computing Over Distributed Sensitive Data and by ERC grant 742754 (project NTSC). The second and forth authors are also supported by ISF grant 152/17, by a grant from the Cyber Security Research Center at Ben-Gurion University of the Negev, and by the Frankel center for computer science. Part of this work was done while the second and forth authors were visiting Simons Institute for the Theory of Computing.
Publisher Copyright:
© 2020 ACM.

PY - 2020/6/8

Y1 - 2020/6/8

N2 - A secret-sharing scheme allows to distribute a secret s among n parties such that only some predefined "authorized" sets of parties can reconstruct the secret, and all other "unauthorized" sets learn nothing about s. 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 2n-o(n) and until recently no better scheme was known. In a recent breakthrough, Liu and Vaikuntanathan (STOC 2018) have reduced the share size to 20.994n+o(n), which was later improved to 20.892n+o(n) by Applebaum et al. (EUROCRYPT 2019). In this paper we improve the exponent of general secret-sharing down to 0.637. For the special case of linear secret-sharing schemes, we get an exponent of 0.762 (compared to 0.942 of Applebaum et al.). As our main building block, we introduce a new robust variant of conditional disclosure of secrets (robust CDS) that achieves unconditional security even under bounded form of re-usability. We show that the problem of general secret-sharing reduces to robust CDS with sub-exponential overhead and derive our main result by implementing robust CDS with a non-trivial exponent. The latter construction follows by presenting a general immunization procedure that turns standard CDS into a robust CDS.

AB - A secret-sharing scheme allows to distribute a secret s among n parties such that only some predefined "authorized" sets of parties can reconstruct the secret, and all other "unauthorized" sets learn nothing about s. 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 2n-o(n) and until recently no better scheme was known. In a recent breakthrough, Liu and Vaikuntanathan (STOC 2018) have reduced the share size to 20.994n+o(n), which was later improved to 20.892n+o(n) by Applebaum et al. (EUROCRYPT 2019). In this paper we improve the exponent of general secret-sharing down to 0.637. For the special case of linear secret-sharing schemes, we get an exponent of 0.762 (compared to 0.942 of Applebaum et al.). As our main building block, we introduce a new robust variant of conditional disclosure of secrets (robust CDS) that achieves unconditional security even under bounded form of re-usability. We show that the problem of general secret-sharing reduces to robust CDS with sub-exponential overhead and derive our main result by implementing robust CDS with a non-trivial exponent. The latter construction follows by presenting a general immunization procedure that turns standard CDS into a robust CDS.

KW - Conditional disclosure of secrets

KW - Robust conditional disclosure of secrets

KW - Secret-sharing schemes

UR - http://www.scopus.com/inward/record.url?scp=85086770468&partnerID=8YFLogxK

U2 - 10.1145/3357713.3384293

DO - 10.1145/3357713.3384293

M3 - Conference contribution

AN - SCOPUS:85086770468

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 280

EP - 293

BT - STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Makarychev, Konstantin

A2 - Makarychev, Yury

A2 - Tulsiani, Madhur

A2 - Kamath, Gautam

A2 - Chuzhoy, Julia

PB - Association for Computing Machinery

T2 - 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020

Y2 - 22 June 2020 through 26 June 2020

ER -