Secure multiplication of shared secrets in the exponent

We present a new protocol for the following task. Given two secrets a, b shared among n players, compute the value gab. The protocol uses the generic BOW approach for multiplication of shared secrets, but we show that if one is computing "multiplications in the exponent" the polynomial randomization step can be avoided (assuming the Decisional Diffie-Hellman Assumption holds). This results in a non-interactive and more efficient protocol. © 2005 Elsevier B.V. All rights reserved.