Questions tagged [lwe]

Learning with Errors is a form of lattice problem used in the design of cryptographic primitives. LWE is based on the Closest Vector Problem (CVP).

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Are LPN and LWE problems equivalent?

Learning with Error (LWE) problem seems like a generalization of Learning Parity with Noise (LPN) problem, where in the latter one uses bits. But, this also makes LPN seem very related to the problem ...
7
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0answers
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Does there exist trapdoor permutation from lattices?

It seems that the lattice functions are either surjective (SIS) or injective (LWE), due to the error that is basically intended to destroy the structure and provide security. I was wondering whether ...
6
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2answers
179 views

LWE: Round a continuous Gaussian to a true Discrete Gaussian

Short version: how is it possible to round a continuous Gaussian into a true discrete Gaussian (usually denoted $\mathcal{D}_{\mathbb{Z},\alpha q}$)? The goal is to obtain a reduction from continuous ...
2
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1answer
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A Simple Provably Secure Key Exchange Scheme Based on the LWE

In this paper (A simple provably secure key exchange by Ding et al.), I am trying to understand the correctness (which is given on page number 8) of the key exchange technique based on LWE. To ...
5
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2answers
221 views

MLWE (and RLWE) to LWE reductions proof

In crypto papers, cryptanalysis of MLWE/RLWE/etc. is often reduced to LWE. Why can we do this? Is there strict proof of such reductions?
4
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1answer
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LWE with identity sub-matrix and reused sampled from [MP12]: why is it secure?

I studied this paper a while ago, but now I'm confused by the paper Trapdoors for Lattices:Simpler, Tighter, Faster, Smaller by Micciancio and Peikert. Page 24 and 25, they present an algorithm that ...