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Ring-LWE in Polynomial Rings [PDF]

Lecture Notes in Computer Science, 2012
The Ring-LWE problem, introduced by Lyubashevsky, Peikert, and Regev (Eurocrypt 2010), has been steadily finding many uses in numerous cryptographic applications. Still, the Ring-LWE problem defined in [LPR10] involves the fractional ideal R ∨, the dual of the ring R , which is the source of many theoretical and implementation technicalities. Until now,
Leo Ducas
exaly   +5 more sources

Efficient Ring-LWE Encryption on 8-Bit AVR Processors [PDF]

Lecture Notes in Computer Science, 2015
Public-key cryptography based on the “ring-variant” of the Learning with Errors (ring-LWE) problem is both efficient and believed to remain secure in a post-quantum world. In this paper, we introduce a carefully-optimized implementation of a ring-LWE encryption scheme for 8-bit AVR processors like the ATxmega128.
Ingrid Verbauwhede, Hwajeong Seo
exaly   +4 more sources

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Lossiness and Entropic Hardness for Ring-LWE

2020
The hardness of the Ring Learning with Errors problem (RLWE) is a central building block for efficiency-oriented lattice-based cryptography. Many applications use an “entropic” variant of the problem where the so-called “secret” is not distributed uniformly as prescribed but instead comes from some distribution with sufficient min-entropy. However, the
Zvika Brakerski, Nico Döttling
openaire   +2 more sources

High-Throughput Ring-LWE Cryptoprocessors

IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2017
This paper presents the design of ring learning with errors (LWE) cryptoprocessors using number theoretic transform (NTT) cores and Gaussian samplers based on the inverse transform method. The NTT cores are designed using radix-2 and radix-8 decimation-in-frequency NTT algorithms and pipeline architectures.
Claudia Patricia Renteria-Mejia, Jaime Velasco-Medina   +1 more
openaire   +2 more sources

FFT Program Generation for Ring LWE-Based Cryptography

2021
Fast Fourier Transform (FFT) enables an efficient implementation of polynomial multiplication, which is at the core of any cryptographic constructions based on the hardness of the Ring learning with errors (RLWE) problem. Existing implementations of FFT for RLWE-based cryptography rely on hand-written assembly code for performance, making it difficult ...
Masahiro Masuda, Yukiyoshi Kameyama
openaire   +1 more source

How (Not) to Instantiate Ring-LWE

2016
The learning with errors over rings Ring-LWE problem--or more accurately, family of problems--has emerged as a promising foundation for cryptography due to its practical efficiency, conjectured quantum resistance, and provable worst-case hardness: breaking certain instantiations of Ring-LWE is at least as hard as quantumly approximating the Shortest ...
openaire   +3 more sources

Large Modulus Ring-LWE $$\ge $$ Module-LWE

2017
We present a reduction from the module learning with errors problem (MLWE) in dimension \(d\) and with modulus \(q\) to the ring learning with errors problem (RLWE) with modulus \(q^{d}\). Our reduction increases the LWE error rate \(\alpha \) by a quadratic factor in the ring dimension \(n\) and a square root in the module rank \(d\) for power-of-two ...
Martin R. Albrecht, Amit Deo
openaire   +2 more sources

Efficient Homomorphic Conversion Between (Ring) LWE Ciphertexts

2021
In the past few years, significant progress on homomorphic encryption (HE) has been made toward both theory and practice. The most promising HE schemes are based on the hardness of the Learning With Errors (LWE) problem or its ring variant (RLWE). In this work, we present new conversion algorithms that switch between different (R)LWE-based HE schemes ...
Hao Chen 0030, Wei Dai 0007, Miran Kim, Yongsoo Song   +3 more
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???????????? ?????????????????? ???????????????????????? ?????????????????????? Ring-LWE ???????????????????????? ?????????? ?? ?????????????????? ???????????????? ??????????????

2023
In terms of application of the generalized BKW algorithm, the estimates of security of Ring-LWE symmetric cryptosystem against chosen plaintext attack have been obtained. These estimates allow us to choose the cryptosystem parameters directly proceeding from requirements of its security against chosen plaintext attacks.
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A Note on Ring-LWE Security in the Case of Fully Homomorphic Encryption

Lecture Notes in Computer Science, 2017
Evaluating the practical security of Ring-LWE based cryptography has attracted lots of efforts recently. Indeed, some differences from the standard LWE problem enable new attacks. In this paper we discuss the security of Ring-LWE as found in Fully Homomorphic Encryption (FHE) schemes. These FHE schemes require parameters of very special shapes, that an
Bonnoron, Guillaume, Fontaine, Caroline
exaly   +4 more sources