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A New Hash-and-Sign Approach and Structure-Preserving Signatures from DLIN

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Security and Cryptography for Networks (SCN 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7485))

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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.

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Authors and Affiliations

  1. Microsoft Research, UK

    Melissa Chase & Markulf Kohlweiss

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  1. Melissa Chase
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  2. Markulf Kohlweiss
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  1. Dipartimento di Informatica, Università di Salerno, via Ponte don Melillo, 84084, Fisciano, SA, Italy

    Ivan Visconti  & Roberto De Prisco  & 

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Chase, M., Kohlweiss, M. (2012). A New Hash-and-Sign Approach and Structure-Preserving Signatures from DLIN. In: Visconti, I., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2012. Lecture Notes in Computer Science, vol 7485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32928-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-32928-9_8

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