Verifiable Signature Sharing Scheme Based on Strong RSA Assumption

Abstract

In 2000, Cramer and Shoup presented a signature scheme which is secure against adaptive chosen-message attacks under the strong RSA assumption in the standard model. Then, in 2003, under the strong RSA assumption only, Fischlin produced a signature of roughly half the length. A verifiable signature sharing scheme (V§S) introduced by Franklin and Reiter in 1995 enables the recipient of a signature to share it among n proxies so that a subset of them can reconstruct it later. In this paper, we first give a modification of Fischlin’s scheme under the strong RSA assumption and then get a new verifiable signature sharing scheme based on it in the standard model. At last, we prove that our new V§S can tolerate the malicious behavior of up to half of the proxies corrupted by a static adversary except for a negligible probability. Our scheme is efficient and the length of signature in our scheme is similar to Fischlin’s and roughly half of Cramer-Shoup signature scheme.