Lattice problems are an attractive basis for cryptographic systems because they seem to offer better security than discrete logarithm and factoring based problems. Efficient lattice-based constructions are known for signature and encryption schemes. However, the constructions known for more sophisticated schemes such as group signatures are still far from being practical. In this paper we make a number of steps towards efficient lattice-based constructions of more complex cryptographic protocols. First, we provide a more efficient way to prove knowledge of plaintexts for lattice-based encryption schemes. We then show how our new protocol can be combined with a proof of knowledge for Pedersen commitments in order to prove that the committed value is the same as the encrypted one. Finally, we make use of this to construct a new group signature scheme that is a “hybrid” in the sense that privacy holds under a lattice-based assumption while security is discrete-logarithm-based.
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- Better Zero-Knowledge Proofs for Lattice Encryption and Their Application to Group Signatures
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