Webfundamental question comes from the Learning Parity with Noise (LPN) problem, which can be seen as LWE with modulus 2 (albeit with a different error distribution), and whose … WebOur reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a quantum algorithm for SVP and SIVP. A main open question is whether this reduction can be made classical. Using the main result, we obtain a public-key cryptosystem whose hardness is based on the worst-case quantum hardness of SVP …

Classical hardness of learning with errors — NYU Scholars

http://malb.io/discrete-subgroup/slides/2024-01-15-deo.pdf WebMay 8, 2016 · The “learning with errors” (LWE) problem is to distinguish random linear equations, which have been perturbed by a small amount of noise, from truly uniform ones, by introducing an algebraic variant of LWE called ring-LWE, and proving that it too enjoys very strong hardness guarantees. 1,858 Highly Influential PDF hejting wikipedia

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WebThe security of all our proposals is provably based (sometimes in the random-oracle model) on the well-studied “learning with errors over rings” problem, and hence on the conjectured worst-case hardness of problems on ideal lattices (against quantum algorithms). WebClassical hardness of learning with errors (STOC 2013) Random Lattices and Lattice Cryptography : Random lattices, the SIS and LWE problems, and construction of basic cryptographic primitives, like one-way functions and collision resistant hashing. WebThen, we sketch the classical hardness proof for LWE and extend the proof techniques to the ring case. We also introduce informal discussions on parameter choices, weaknesses, related work, and open problems. Key words: Learning with Errors, Ring Learning with Errors, Lattices, Lattice-based Cryptography, Post-quantum Cryptography. 1 he junfeng lab