Efficient Group Signature Scheme Over NTRU Lattice

Group signature schemes empower users to sign messages in the name of a group at the same time (1) keeping anonymity with respect to an outsider, and (2) guaranteeing traceability of a signer when needed. In this work we construct a new group signature scheme based on NTRU lattices. To achieve goals, we use a new algorithm for sampling a basis on NTRU lattice. Group signatures have many features, such as anonymity and traceability. They play an important role in the field of cryptography, and group-based group signatures are more resistant to quantum attacks. However, the unique advantages of lattice cryptography have the disadvantage of space consumption. At present the group signature schemes has high communication cost, and their size of system public key size is too large. Hence NTRU lattice is a kind of special lattice based on polynomial ring, and only involves polynomial ring small integer multiplication and modular arithmetic compared with the general case. NTRU lattice system shortens the length of public key, and has the faster computing speed. In order to reduce the size of the lattice key, this paper uses the Gaussian discrete distributed sampling algorithm on the NTRU lattice to construct a new NTRU lattice-based group signature. And provide relevant safety certification and efficiency analysis.