In this work we apply information theoretically optimal arithmetic coding and a number of novel side-channel blinding countermeasure techniques to create BLZZRD, a practical, compact, and more quantum-resistant variant of the BLISS Ring-LWE Signature Scheme. We show how the hash-based random oracle can be modified to be more secure against quantum preimage attacks while decreasing signature siz...

The security of pairing-based cryptography is based on the hardness of solving the discrete logarithm problem (DLP) over extension field GF(p) of characteristic p and degree n. Joux et al. proposed an asymptotically fastest algorithm for solving DLP over GF(p) (JLSV06-NFS) as the extension of the number field sieve over prime field GF(p) (JL03-NFS). The lattice sieve is often used for a largesc...

This paper presents a low-latency hardware accelerator for modular polynomial multiplication lattice-based post-quantum cryptography and homomorphic encryption applications. The proposed novel multiplier exploits the fast finite impulse response (FIR) filter architecture to reduce computational complexity of schoolbook multiplication. We also extend this structure $M$-parallel architectures whi...

Homomorphic Encryption is a recent promising tool in modern cryptography, that allows to carry out operations on encrypted data. In this paper we focus on the design of a scheme based on pairings and elliptic curves, that is able to handle applications where the number of multiplication is not too high, with interesting practical efficiency when compared to lattice based solutions. The starting...

We prove the equivalence, up to a small polynomial approximation factor √ n/ log n, of the lattice problems uSVP (unique Shortest Vector Problem), BDD (Bounded Distance Decoding) and GapSVP (the decision version of the Shortest Vector Problem). This resolves a long-standing open problem about the relationship between uSVP and the more standard GapSVP, as well the BDD problem commonly used in co...

Succinct non-interactive arguments (SNARGs) enable verifying NP computations with substantially lower complexity than that required for classical NP verification. In this work, we first construct a lattice-based SNARG candidate with quasi-optimal succinctness (where the argument size is quasilinear in the security parameter). Further extension of our methods yields the first SNARG (from any ass...

We describe new arithmetic coding techniques and side-channel blinding countermeasures for lattice-based cryptography. Using these techniques, we develop a practical, compact, and more quantum-resistant variant of the BLISS Ideal Lattice Signature Scheme. We first show how the BLISS parameters and hash-based random oracle can be modified to be more secure against quantum preimage attacks while ...

Residuation is a fundamental concept of ordered structures and categories. In this survey we consider the consequences of adding a residuated monoid operation to lattices. The resulting residuated lattices have been studied in several branches of mathematics, including the areas of lattice-ordered groups, ideal lattices of rings, linear logic and multi-valued logic. Our exposition aims to cover...