A Lightweight Public Verifiable Multi Secret Sharing Scheme Using Short Integer Solution

Abstract

In this paper we introduce a multi secret sharing (MSS) scheme based on lattice conception. Lattice constitutes the core of many cryptographic constructions. The advantage of using lattice, which our scheme will inherit, is twofold: first is that the hardness of lattice problems is well understood. We will show that breaking our scheme leads to a solution for the robust Short Integer Solution problem. Hence, the presented scheme's security is guaranteed by leveraging lattice based conceptions. Second advantage is that working with lattice is simple and, consequently, execution is fast. A main problem with previous schemes is that they mostly are based on numerical assumptions which are slow and need much throughput. Inheriting simplicity and fastness make our scheme an excellent choice to implement in facilities with limit computational power and resources. In secret sharing schemes, typically in any protocol, dishonest participants and dealer can cheat during execution. To mitigate these concerns we augment our scheme with verifiability properties, say verifiable and public verifiable secret sharing. Verifiability prevents the dealer to share wrong shares and public verifiability forces participants to submit their sub-shares correctly. In MSS schemes, releasing some public values which are used in recovering step is inevitable. At the end, a comprehensive comparison by a table in the conclusion section shows that the presented scheme has minimum number of public values among MSS schemes.