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Introduction
In August 13th, 2024, NIST announced three post-quantum cryptography standards, where two of them are from lattice-based cryptography and the other one is from hash-based cryptography. In this post, we will have an overview about FIPS 203, which specify algorithms derived from CRYSTALS-Kyber, is a key encapsulation mechanism based on module lattice.
Notation
Pre-requisited
The LWE Problem
Definition
The Learning with Errors Problem (LWE) has an important role in many cryptographic schemes that are related to lattice cryptography, so let's review this problem again.
Definition 1. For positive integer $m, n, q$ and $\beta < q$, the $LWE_{n, m, q, \beta}$ problem asks to distinguish between the following two distributions: