Homomorphisms of Secret Sharing Schemes: A Tool for Verifiable Signature Sharing

Franklin and Reiter introduced at Eurocrypt '95 verifiable signature sharing, a primitive for a fault tolerant distribution of signature verification. They proposed various praclical protocols. For RSA signatures with exponent e = 3 and n processors their protocol allows for up to (n 1)/5 faulty processors (in general (n 1)/(2 + e)). We consider a new unifying approach which uses homomorphisms of secret sharing schemes, and present a verifiable signature sharing scheme for which as many as (n 1)/3 processors can be faulty (for any value of e) , and for which the number of interactions is reduced.