Chapter

Advances in Cryptology – CRYPTO 2013

Volume 8043 of the series Lecture Notes in Computer Science pp 289-307

Linearly Homomorphic Structure-Preserving Signatures and Their Applications

  • Benoît LibertAffiliated withTechnicolor
  • , Thomas PetersAffiliated withCrypto Group, Université catholique de Louvain
  • , Marc JoyeAffiliated withTechnicolor
  • , Moti YungAffiliated withGoogle Inc. and Columbia University

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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.

Keywords

Structure-preserving cryptography signatures homomorphism commitment schemes non-malleability