Related papers: Provably weak instances of Ring-LWE

Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with…

We discuss the advantages and limitations of cyclotomic fields to have fast polynomial arithmetic within homomorphic encryption, and show how these limitations can be overcome by replacing cyclotomic fields by a family that we refer to as…

We show direct and conceptually simple reductions between the classical learning with errors (LWE) problem and its continuous analog, CLWE (Bruna, Regev, Song and Tang, STOC 2021). This allows us to bring to bear the powerful machinery of…

Learning with Errors (LWE) is a hard math problem used in post-quantum cryptography. Homomorphic Encryption (HE) schemes rely on the hardness of the LWE problem for their security, and two LWE-based cryptosystems were recently standardized…

The Learning with Errors (LWE) problem is a hard math problem in lattice-based cryptography. In the simplest case of binary secrets, it is the subset sum problem, with error. Effective ML attacks on LWE were demonstrated in the case of…

We describe a decisional attack against a version of the PLWE problem in which the samples are taken from a certain proper subring of large dimension of the cyclotomic ring $\mathbb{F}_q[x]/(\Phi_{p^k}(x))$ with $k>1$ in the case where…

We prove that the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems over the cyclotomic field $\mathbb{Q}(\zeta_n)$ are not equivalent. Precisely, we show that reducing one problem to the other…

Sparse binary LWE secrets are under consideration for standardization for Homomorphic Encryption and its applications to private computation. Known attacks on sparse binary LWE secrets include the sparse dual attack and the hybrid sparse…

Learning with Errors (LWE) is a hard math problem underpinning many proposed post-quantum cryptographic (PQC) systems. The only PQC Key Exchange Mechanism (KEM) standardized by NIST is based on module~LWE, and current publicly available PQ…

Block ciphers are in widespread use since the 1970s. Their iterated structure is prone to numerous round invariant attacks for example in Linear Cryptanalysis (LC). The next step is to look at non-linear polynomial invariants cf.…

Currently deployed public-key cryptosystems will be vulnerable to attacks by full-scale quantum computers. Consequently, "quantum resistant" cryptosystems are in high demand, and lattice-based cryptosystems, based on a hard problem known as…

Learning with Errors (LWE) is a hard math problem underlying recently standardized post-quantum cryptography (PQC) systems for key exchange and digital signatures. Prior work proposed new machine learning (ML)-based attacks on LWE problems…

Linear (or differential) cryptanalysis may seem dull topics for a mathematician: they are about super simple invariants characterized by say a word on n=64 bits with very few bits at 1, the space of possible attacks is small, and basic…

The Learning with Errors (LWE) problem underlies modern lattice-based cryptography and is assumed to be quantum hard. Recent results show that estimating entanglement entropy is as hard as LWE, creating tension with quantum gravity and…

In this paper, we propose an encrypted dynamic controller that executes an unlimited number of recursive homomorphic multiplications on a Ring Learning With Errors (Ring-LWE) based cryptosystem without bootstrapping. The proposed controller…

We study the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for cyclotomic number fields,namely: we prove that both problems are equivalent via a polynomial noise increase as long as the…

Any ideal in a number field can be factored into a product of prime ideals. In this paper we study the prime ideal shortest vector problem (SVP) in the ring $ \Z[x]/(x^{2^n} + 1) $, a popular choice in the design of ideal lattice based…

We provide a reduction of the Ring-LWE problem to Ring-LWE problems in subrings, in the presence of samples of a restricted form (i.e. $(a,b)$ such that $a$ is restricted to a multiplicative coset of the subring). To create and exploit such…

LWE-based cryptosystems are an attractive alternative to traditional ones in the post-quantum era. To minimize the storage cost of part of its public key - a $256 \times 640$ integer matrix, $\textbf{T}$ - a binary version of $\textbf{T}$…

Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus,…