Secure multiplication of shared secrets in the exponent

Authors:
Rosario Gennaro;Mario Di Raimondo
Affiliations:
IBM T.J. Watson Research Center, Yorktown Heights, NY;Dipartimento di Matematica e Informatica, Università di Catania, Italy
Venue:
Information Processing Letters
Year:
2005

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Abstract

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 BGW 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.