Multiparty secret sharing based on hidden multipliers
This addresses the need for efficient and secure multiparty secret sharing in cryptography, though it appears incremental as it builds on existing concepts with a specific new property.
The paper tackles the problem of designing secret sharing schemes that allow shares to be reused multiple times, proposing schemes based on hidden multipliers in encryption that are semantically secure and enable the same message to be transmitted in different forms without revealing which secret was transferred.
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.