A new hash-and-sign approach and structure-preserving signatures from DLIN

  • Authors:
  • Melissa Chase;Markulf Kohlweiss

  • Affiliations:
  • Microsoft Research, UK;Microsoft Research, UK

  • Venue:
  • SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
  • Year:
  • 2012

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Abstract

Suppose we have a signature scheme for signing elements of message space $\mathcal{M}_1$, but we need to sign messages from $\mathcal{M}_2$. The traditional approach of applying a collision resistant hash function from $\mathcal{M}_1$ to $\mathcal{M}_2$ can be inconvenient when the signature scheme is used within more complex protocols, for example if we want to prove knowledge of a signature. Here, we present an alternative approach in which we can combine a signature for $\mathcal{M}_1$, a pairwise independent hash function with key space $\mathcal{M}_1$ and message space $\mathcal{M}_2$, and a non-interactive zero knowledge proof system to obtain a signature scheme for message space $\mathcal{M}_2$. This transform also removes any dependence on state in the signature for $\mathcal{M}_1$. As a result of our transformation we obtain a new signature scheme for signing a vector of group elements that is based only on the decisional linear assumption (DLIN). Moreover, the public keys and signatures of our scheme consist of group elements only, and a signature is verified by evaluating a set of pairing-product equations, so the result is a structure-preserving signature. In combination with the Groth-Sahai proof system, such a signature scheme is an ideal building block for many privacy-enhancing protocols.