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In post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption.
The ring learning with errors key exchange (RLWE-KEX) is one of a new class of public key exchange algorithms that are designed to be secure against an adversary that possesses a quantum computer. This is important because some public key algorithms in use today will be easily broken by a quantum computer if such computers are implemented.
The creators of the Ring-based Learning with Errors (RLWE) basis for cryptography believe that an important feature of these algorithms based on Ring-Learning with Errors is their provable reduction to known hard problems. [8] [9] The signature described below has a provable reduction to the Shortest Vector Problem in an ideal lattice. [10]
Selected schemes for the purpose of key exchange, also called key establishment, key encapsulation and key encapsulation mechanism (KEM): CRYSTALS-Kyber, [19] which is built upon module learning with errors (module-LWE). Kyber was selected for standardization by the NIST in 2023. [1]
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]
“It wasn’t his fault,” Luke Devaney clarifies. “I think people afterwards were saying, ‘Good job, Will, you misplaced the rings.’ He played it off.
This approach includes cryptographic systems such as learning with errors, ring learning with errors (), [14] [15] [16] the ring learning with errors key exchange and the ring learning with errors signature, the older NTRU or GGH encryption schemes, and the newer NTRU signature and BLISS signatures. [17]
In post-quantum cryptography, NewHope is a key-agreement protocol by Erdem Alkim, Léo Ducas, Thomas Pöppelmann, and Peter Schwabe that is designed to resist quantum computer attacks. [ 1 ] [ 2 ] NewHope is based on a mathematical problem ring learning with errors (RLWE) that is believed to be difficult to solve.