Over the last years lattice-based cryptography has received much attention due to versatile average-case problems like Ring-LWE or Ring-SIS that appear to be intractable by quantum computers. But despite of promising constructions, only few results have been published on implementation issues on very constrained platforms. In this work we therefore study and compare implementations of Ring-LWE ...

The security of many cryptographic schemes has been based on special instances of the Learning with Errors (LWE) problem, e.g., Ring-LWE, LWE with binary secret, or LWE with ternary error. However, recent results show that some subclasses are weaker than expected. In this work we show that LWE with binary error, introduced by Micciancio and Peikert, is one such subclass. We achieve this by appl...

Many practical lattice-based schemes are built upon the Ring-SIS or Ring-LWE problems, which are problems that are based on the presumed difficulty of finding low-weight solutions to linear equations over polynomial rings Zq[x]/〈f〉. Our belief in the asymptotic computational hardness of these problems rests in part on the fact that there are reduction showing that solving them is as hard as fin...

The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms for the principal ideal SVP problem, and attempts to generalize the attack to non-principal ideals. In this work, we study the LWE problem on group rings, a...

Cryptography based on lattices is the use of conjectured hard problems on point lattices in Rn as the basis for security in cryptosystems. In this report, firstly we introduce lattices and some hard problems based on lattice then present some of the major developments in lattice-based cryptography. The main focus in this report is on the fundamental learning with errors (LWE) problems, Ring-LWE...

Significant innovation has been made in the development of public-key cryptography that is able to withstand quantum attacks, known as post-quantum (PQC). This paper focuses on an efficient PQC hardware implementation. Specifically, implementation binary Ring-learning-with-errors (BRLWE)-based encryption scheme, a promising lightweight suitable for resource-constrained applications, proposed. T...

In this short note we observe that the Peikert-Vaikuntanathan-Waters (PVW) method of packing many plaintext elements in a single Regev-type ciphertext, can be used for performing SIMD homomorphic operations on packed ciphertext. This provides an alternative to the Smart-Vercauteren (SV) ciphertextpacking technique that relies on polynomial-CRT. While the SV technique is only applicable to schem...

This study is the first to investigate novel cone lasers and the tunabilities of their lasing feature and performance based on dye-doped cholesteric liquid crystal (DDCLC) films with various LC birefringences (Δn). A unique conically-symmetric lasing ring with a low energy threshold occurs at a specific nonzero oblique angle (θ(ring)). The low energy threshold is comparable to those for common ...

The Ring-LWE (RLWE) problem is expected to be a computationally-hard problem even with quantum algorithms. The Poly-LWE (PLWE) problem is closely related to the RLWE problem, and in practice a security base for various recently-proposed cryptosystems. In 2014, Eisentraeger et al. proposed attacks against the decision-variant of the PLWE problem (and in 2015, Elias et al. precisely described and...

Compact implementations of the ring variant of the Learning with Errors (Ring-LWE) on the embedded processors have been actively studied due to potential quantum threats. Various Ring-LWE implementation works mainly focused on optimization techniques to reduce the execution timing and memory consumptions for high availability. For this reason, they failed to provide secure implementations again...