Robust Additive Secret Sharing Schemes over Zm

In a threshold secret sharing scheme, a dishonest participant can disrupt the operation of the system by submitting junk instead of his/her share. We propose two constructions for threshold secret sharing schemes that allow identification of cheaters where the secret is an element of the ringZ m . The main motivation of this work is to design RSA-based threshold cryptosystems, such as robust threshold RSA signature, in which additive (multiplicative) threshold secret sharing schemes over Abelian groups with cheater identification play the central role. The first construction extends Desmedt-Frankel’s construction of secret sharing over Z m to provide cheater detection, and the second construction uses perfect hash families to construct a robust (t, n) scheme from a (t, t) scheme. We prove security of these schemes and assess their performance.

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