Compact Verifiably Multiplicative Secret Sharing

• Maki Yoshida

  National Institute of Information and Communications Technology

• Satoshi Obana

  Hosei University

Abstract

A $d$-multiplicative secret sharing ($d$-MSS) scheme over a finite field allows the players to multiply $d$ shared secrets without recovering the secrets by converting their shares {\em locally} into an {\em additive} sharing of the product [Journal of Cryptology, 2010]. A verifiably $d$-MSS ($d$-VMSS) further enables the players to locally generate an {\em additive} sharing of a {\em proof} that the output (rather than each share) is correct [IEEE Trans.\ on Information Theory, 2019]. In the most efficient construction known so far, while a share of the output is a single element of the finite field, a proof of correctness consists of two or more elements. In this paper, we study (in)feasibility of a single-element proof of correctness. First, we derive a sufficient condition on a proof-generation function, referred to as <br>{\em multiplicative-only homomorphism (MoH)}. Secondly, we show the concrete family of MoHs, meaning that the condition is satisfied. Then, we present a generic construction of $d$-VMSS from any $d$-MSS and any MoH. Finally, we show concrete instantiations of $d$-VMSS that realize a single-element proof of correctness.

Journal

• IEICE Proceeding Series

  IEICE Proceeding Series 65 437-441, 2020-10-18

  The Institute of Electronics, Information and Communication Engineers

Keywords

• secret sharing
• multiplicative
• verifiable
• compact

Details

• CRID: 1390569148830844416
• NII Article ID: 230000012690
• DOI: 10.34385/proc.65.c03-4
• ISSN: 21885079
• Text Lang: en
• Data Source:
  • JaLC
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed