This work presents a multilevel approximation exploration undertaken on the Ring-Learning-with-Errors (R-LWE)-based public-key cryptographic (PKC) schemes that belong to quantum-resilient cryptography algorithms. Among various proposed in currently running NIST’s post-quantum (PQC) standardization plan, lattice-based learning-with-error (LWE) have emerged as most viable and preferred class for ...

In this paper we port Brakerski’s fully homomorphic scheme based on the Learning With Errors (LWE) problem to the ring-LWE setting. We introduce two optimised versions of relinearisation that not only result in a smaller relinearisation key, but also faster computations. We provide a detailed, but simple analysis of the various homomorphic operations, such as multiplication, relinearisation and...

In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems [EHL, ELOS] gives rise to interesting questions about number fields. We extend these attacks and survey related open problems in number theory, including spectral distortion of an algebraic number and its relationship to Mahler me...

Abstract In this paper, we construct multi-key homomorphic and fully encryption (resp. MKHE MKFHE) schemes with malicious circuit privacy. Our are based on learning errors (LWE) besides appropriate circular security assumptions. contrast, the previous maliciously circuit-private MKFHE scheme by Chongchitmate Ostrovsky (PKC, 2017) is non-standard decisional small polynomial ratio (DSPR) assumpti...

Abstract As quantum computing advances rapidly, guaranteeing the security of cryptographic protocols resistant to attacks is paramount. Some leading candidate cryptosystems use learning with errors (LWE) problem, attractive for its simplicity and hardness guaranteed by reductions from hard computational lattice problems. Its algebraic variants, ring-learning (RLWE) polynomial (PLWE), gain effic...

We describe a new reconciliation method for Ring-LWE that has a significantly smaller failure rate than previous proposals while reducing ciphertext size and the amount of randomness required. It is based on a simple, deterministic variant of Peikert’s reconciliation that works with our new “safe bits” selection and constant-time error correction techniques. The new method does not need randomi...

Recently, ARM NEON architecture has occupied a significant share of tablet and smartphone markets due to its low cost and high performance. This paper studies efficient techniques of lattice-based cryptography on ARM processor and presents the first implementation of ring-LWE encryption on ARM NEON architecture. In particular, we propose a vectorized version of Iterative Number Theoretic Transf...

Some lattice-based public key cryptosystems allow one to transform ciphertext from one lattice or ring representation to another e ciently and without knowledge of public and private keys. In this work we explore this lattice transformation property from cryptographic engineering viewpoint. We apply ciphertext transformation to compress Ring-LWE ciphertexts and to enable e cient decryption on a...

Recent advances in lattice cryptography, mainly stemming from the development of ring-based primitives such as ring-LWE, have made it possible to design cryptographic schemes whose efficiency is competitive with that of more traditional number-theoretic ones, along with entirely new applications like fully homomorphic encryption. Unfortunately, realizing the full potential of ring-based cryptog...

The decision Learning With Errors problem has proven an extremely flexible foundation for devising provably secure cryptographic primitives. LWE can be expressed in terms of linear algebra over Z/qZ. This modulus q is the subject of study of the present work. When q is prime and small, or when it is exponential and composite with small factors, LWE is known to be at least as hard as standard wo...