A new lattice-based online/offline signatures framework for low-power devices

Lattice-based online/offline signature scheme enjoys the advantage of resisting quantum feature besides the short online response time. The existing Fiat-Shamir with aborts paradigm candidates do not have perfect online/offline property, and the hash-sign-switch ones usually increase the signature sizes. In this paper we mainly address its online time and the length of signature issues, and propose a new and efficient paradigm of its construction for lattice assumptions over rings. In this paradigm the signer tries to sign for a random string and the message respectively. Specifically, we first discuss the generic construction of Fiat-Shamir lattice-based signatures. Then for a large class of lattice-based relations over rings, we propose an improved framework designed for low-power devices. This new framework allows the signer to extract a part of the signature only for a random string chosen in offline time, and thus can obtain the whole signature by less online time. In addition, the resulting scheme slightly reduces the signature size compared to the Fiat-Shamir counterparts. The performance analysis shows that our construction is efficient.