Computing Inverses over a Shared Secret Modulus

We discuss the following problem: Given an integer shared secretly among n players and a prime number e, how can the players efficiently compute a sharing of e-1 mod . The most interesting case is when is the Euler function of a known RSA modulus N, = (N). The problem has several applications, among which the construction of threshold variants for two recent signature schemes proposed by Gennaro-Halevi-Rabin and Cramer-Shoup. We present new and efficient protocols to solve this problem, improving over previous solutions by Boneh-Franklin and Frankel et al. Our basic protocol (secure against honest but curious players) requires only two rounds of communication and a single GCD computation. The robust protocol (secure against malicious players) adds only a couple of rounds and a few modular exponentiations to the computation.

• Type: Conference
• Year: 2000
• Where: EUROCRYPT
• Authors: Dario Catalano, Rosario Gennaro, Shai Halevi
• Keywords: Cryptology, E-1 Mod, EUROCRYPT 2000, Prime Number E, Single Gcd Computation