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Learning with errors - Wikipedia

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In cryptography, learning with errors (LWE) is a mathematical problem that is widely used to create secure encryption algorithms.[1] It is based on the idea of representing secret information as a set of equations with errors. In other words, LWE is a way to hide the value of a secret by introducing noise to it.[2] In more technical terms, it refers to the computational problem of inferring a linear 𝑛 -ary function 𝑓 over a finite ring from given samples 𝑦 𝑖 = 𝑓 ( 𝑥 𝑖 ) some of which may be erroneous. The LWE problem is conjectured to be hard to solve,[1] and thus to be useful in cryptography. More precisely, the LWE problem is defined as follows. Let 𝑍 𝑞 denote the ring of integers modulo 𝑞 and let 𝑍 𝑞 𝑛 denote the set of 𝑛 -vectors over 𝑍 𝑞 . There exists a certain unknown linear function 𝑓 : 𝑍 𝑞 𝑛 → 𝑍 𝑞 , and the input to the LWE problem is a sample of pairs ( 𝑥 , 𝑦 ) , where 𝑥 ∈ 𝑍 𝑞 𝑛 and 𝑦 ∈ 𝑍 𝑞 , so that with high probability 𝑦 =

Learning with errors - Wikipedia Jump to content From Wikipedia, the free encyclopedia Mathematical problem in cryptography This article may be too technical for most readers to understand . Please help improve it to make it understandable to non-experts , without removing the technical details. ( October 2018 ) ( Learn how and when to remove this message ) In cryptography , learning with errors ( LWE ) is a mathematical problem that is widely used to create secure encryption algorithms . [ 1 ] It is based on the idea of representing secret information as a set of equations with errors. In oth

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