Cryptology ePrint Archive: Report 2009/007

Homomorphic Trapdoor Commitments to Group Elements

Jens Groth

Abstract: We present a homomorphic trapdoor commitment to group elements. In contrast, previous homomorphic trapdoor commitment schemes only allow the messages to be exponents. Our commitment scheme is length-reducing, we can make a short commitment to many group elements at once, and it is perfectly hiding and computationally binding. The construction is based on groups with a bilinear map and the binding property follows from the simultaneous triple pairing assumption. While the simultaneous triple pairing assumption is new, we demonstrate that it is implied by the well-known decision linear assumption.

Category / Keywords: public-key cryptography / homomorphic trapdoor commitment, bilinear groups, simultaneous triple pairing assumption

Date: received 3 Jan 2009

Contact author: j groth at ucl ac uk

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Version: 20090104:222843 (All versions of this report)

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