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 (first version) based on the performance of state-of-the-art lattice reduction and enumeration tech- niques. In the revision, we re-evaluate the security of first version of the parameter sets, under the hybrid approach of lattice reduction attack the meet-in-the-middle attack. We present new sets of parameters that are robust against this attack, as well as all previous known attacks

Choosing Parameters for NTRUEncrypt

We describe a methods for generating parameter sets and calculating security estimates for NTRUEncrypt. Analyses are provided for the standardized product-form parameter sets from IEEE 1363.1-2008 and for the NTRU Challenge parameter sets

DA-Encrypt: Homomorphic Encryption via Non-Archimedean Diophantine Approximation --- Preliminary Report

We give a theoretical description of a new homomorphic encryption scheme DA-Encrypt that is based on (non-archimedean) Diophantine Approximation