Learning With Errors (LWE) and Ring LWE
The method describing LWE is defined here.
Learning With Errors (LWE) is a quantum robust method of cryptography. It is also used within homomorphic encryption. Initially we create a secret key value (s) and another value (e). Next we select a number of values (A[]) and calculate B[] = A[] x s + e. The values of A[] and B[] become our public key. If s is a single value, A and B are one dimensional matrices. If we select s to be a one-dimensional matrix, A will be a two-dimensional matrix, and B will be a one-dimensional matrix.
Outline
Learning with errors is a method defined by Oded Regev in 2005 [here] and is known as LWE (Learning With Errors). It involves the difficulty of finding the values which solve:
B=A×s+e
where you know A and B. The value of s becomes the secret values (or the secret key), and A and B can become the public key.
Slides: [here]
