Quantum-Resistant Forward-Secure Digital Signature Scheme Based on q-ary Lattices

In this paper, we design and consider a new digital signature scheme with an evolving secret key, using random q-ary lattices as its domain. It is proved that, in addition to offering classic eu-cma security, the scheme is existentially forward unforgeable under an adaptive chosen message attack (fu-cma). We also prove that the secret keys are updated without revealing anything about any of the keys from the prior periods. Therefore, we design a polynomial-time reduction and use it to show that the ability to create a forgery leads to a feasible method of solving the well-known small integer solution (SIS) problem. Since the security of the scheme is based on computational hardness of a SIS problem, it turns out to be resistant to both classic and quantum methods. In addition, the scheme is based on the "Fiat-Shamir with aborts" approach that foils a transcript attack. As for the key-updating mechanism, it is based on selected properties of binary trees, with the number of leaves being the same as the number of time periods in the scheme. Forward security is gained under the assumption that one out of two hash functions is modeled as a random oracle.