Transcript Secure Signatures Based On Modular Lattices

We introduce a class of lattice-based digital signature schemes based on modular properties of the coordinates of lattice vectors. We also suggest a method of making such schemes transcript secure via a rejection sampling technique of Lyubashevsky (2009). A particular instantiation of this approach is given, using NTRU lattices. Although the scheme is not supported by a formal security reduction, we present arguments for its security and derive concrete parameters based on the performance of state-of-the-art lattice reduction and enumeration techniques.