Multiparty secret sharing based on hidden multipliers

TL;DR

This paper introduces novel multiparty secret sharing schemes utilizing hidden multipliers within algebraic structures, enabling multiple uses of shares and ensuring semantic security, with practical numerical examples provided.

Contribution

It presents new secret sharing schemes based on hidden multipliers that allow multiple share usages and semantic security, expanding the cryptographic toolkit.

Findings

Shares can be reused multiple times without re-distribution.

Schemes are semantically secure, preventing secret inference.

Numerical examples demonstrate practical implementation.

Abstract

Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular, multiplicative groups of residue rings. We propose two versions of the secret sharing scheme and a version of ($k,n$)-thrested scheme. For a given $n$, the dealer can choose any $k.$ The main feature of the proposed schemes is that the shares of secrets are distributed once and can be used multiple times. This property distinguishes the proposed schemes from the secret sharing schemes known in the literature. The proposed schemes are semantically secure. The same message can be transmitted in different forms. From the transferred secret $c$ it is impossible to determine which of the two given secrets $m_1$ or $m_2$ was transferred. For concreteness, we give some numerical examples.