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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 fundamental idea of using LWE and Ring LWE for key exchange was proposed and filed at the University of Cincinnati in 2011 by Jintai Ding. The basic idea comes from the associativity of matrix multiplications, and the errors are used to provide the security.
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]
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 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]
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]
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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.