Recent research in the field of lattice-based cryptography, especially on the topic of the ring-based primitive ring-LWE, provided efficient and practical ring-based cryptographic schemes, which can compete with more traditional number-theoretic ones. In the case of ring-LWE these cryptographic schemes operated mainly in power-of-two cyclotomics, which vastly restricted the variety of possible ...

Public key exchange protocol is identified as an important application in the field of public-key cryptography. Most of the existing public key exchange schemes are Diffie-Hellman (DH)-type, whose security is based on DH problems over different groups. Note that there exists Shor’s polynomial-time algorithm to solve these DH problems when a quantum computer is available, we are therefore motiva...

The NTRU public-key cryptosystem, proposed in 1996 by Hoffstein, Pipher and Silverman, is a fast and practical alternative to classical schemes based on factorization or discrete logarithms. In contrast to the latter schemes, it offers quasi-optimal asymptotic efficiency and conjectured security against quantum computing attacks. The scheme is defined over finite polynomial rings, and its secur...

In 2016, the National Institute of Standards and Technology (NIST) announced an open competition with goal finding standardizing suitable algorithms for quantum-resistant cryptography. This study presents a detailed, mathematically oriented overview round-three finalists NIST’s post-quantum cryptography standardization consisting lattice-based key encapsulation mechanisms (KEMs) CRYSTALS-Kyber,...

Compared to the classical cryptography, lattice-based cryptography is more secure, flexible and simple, and it is believed to be secure against quantum computers. In this paper, an efficient signature scheme is proposed from the ring learning with errors (R-LWE), which avoids sampling from discrete Gaussians and has the characteristics of the much simpler description etc. Then, the scheme is im...

Inspired by quantum annealing, digital annealing computers specified for computations have been realized on a large scale, such as the Digital Annealer (DA) developed Fujitsu and CMOS Annealing Machine Hitachi. With progress achieved using these computers, it has become necessary to estimate computational hardness of cryptographic problems. This paper focuses lattice problems, closest vector pr...

Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...