Cryptology ePrint Archive: Report 2013/361

Linearly Homomorphic Structure-Preserving Signatures and Their Applications

Benoit Libert and Thomas Peters and Marc Joye and Moti Yung

Abstract: Structure-preserving signatures (SPS) are signature schemes where messages, signatures and public keys all consist of elements of a group over which a bilinear map is efficiently computable. This property makes them useful in cryptographic protocols as they nicely compose with other algebraic tools (like the celebrated Groth-Sahai proof systems). In this paper, we consider SPS systems with homomorphic properties and suggest applications that have not been provided before (in particular, not by employing ordinary SPS). We build linearly homomorphic structure-preserving signatures under simple assumptions and show that the primitive makes it possible to verify the calculations performed by a server on outsourced encrypted data (i.e., combining secure computation and authenticated computation to allow reliable and secure cloud storage and computation, while freeing the client from retaining cleartext storage). Then, we give a generic construction of non-malleable (and actually simulation-sound) commitment from any linearly homomorphic SPS. This notably provides the first constant-size non-malleable commitment to group elements.

Category / Keywords: public-key cryptography / Structure-preserving cryptography, signatures, homomorphism, commitment schemes, non-malleability

Publication Info: Crypto 2013 -- This is the full version

Date: received 8 Jun 2013, last revised 17 Jul 2013

Contact author: benoit libert at technicolor com

Available format(s): PDF | BibTeX Citation

Note: Fixed one issue in Appendix B

Version: 20130717:182901 (All versions of this report)

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