The Wonderful Ring Learning With Errors (RLWE) and Homomorphic Encryption

We live in a computing world which has really changed much from the computing model defined by Von Numan. Basically all our data bits can be observed in some way, and which exposes our data at the lower levels, such as in the memory and the processor. But, a new world awaits, and it is one where we encrypt the data at its source, and then can still process it in an encrypted form. This is the wonderful world of Ring Learning With Errors (RLWE) and homomorphic encryption.

Homomorphic encryption supports mathematical operations on encrypted values. Partial Homomorphic Encryption (PHE) supports a few arithmetic operations, while Full Homomorphic Encryption (FHE) supports add, subtract, multiply, and divide. Homomorphic encryption normally involves a public key to encrypt the data, and a private key to decrypt it. There have been four main generations of homomorphic encryption, and the most recent being the CKKS method.

Introduction

Homomorphic encryption supports mathematical operations on encrypted data. In 1978, Rivest, Adleman, and Dertouzos [2] were the first to define the possibilities of implementing a homomorphic operation and used the RSA method. This supported multiply and divide operations [here], but does not support addition and subtraction. Overall…