IACR News item: 17 September 2015
Alonso González, Alejandro Hevia, Carla Ràfols
ePrint ReportIn this paper we develop specific techniques for asymmetric groups. We introduce a new computational assumption, under which we can recover all the aggregation results of Groth- Sahai proofs known in the symmetric setting. We adapt the arguments of membership in linear spaces of $G^m$ to linear subspaces of $G^m \\times H^n . In particular, we give a constant-size argument that two sets of Groth-Sahai commitments, defined over different groups $G$, $H$, open to the same scalars in $Z_q$, a useful tool to prove satisfiability of quadratic equations in $Z_q$. We then use one of the arguments for subspaces in $G^m \\times H^n$ and develop new techniques to give constant-size QA-NIZK proofs that a commitment opens to a bit-string. To the best of our knowledge, these are the first constant-size proofs for quadratic equations in $Z_q$ under standard and falsifiable assumptions. As a result, we obtain improved threshold Groth-Sahai proofs for pairing product equations, ring signatures, proofs of membership in a list, and various types of signature schemes.
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