What is Homomorphic Encryption?

Homomorphic encryptions allow complex mathematical operations to be performed on encrypted data without compromising the encryption. In mathematics, homomorphic describes the transformation of one data set into another while preserving relationships between elements in both sets. The term is derived from the Greek words for 'same structure.' Because the data in a homomorphic encryption scheme retains the same structure, identical mathematical operations -- whether they are performed on encrypted or decrypted data -- will yield equivalent results.

Homomorphic encryption is expected to play an important part in cloud computing, allowing companies to store encrypted data in a public cloud and take advantage of the cloud provider's analytic services. (Rouse)

Equation

E(A)+E(B)=E(C)=E(A+B) and D(E(A+B))=A+B

Motivation

This website will serve as an interactive introduction into the homomorphic properties of Shamir's Secret Sharing for future students studying cryptographic strategies. As stated in one paper studying the impact of interactive websites on learning, "Using features which promote...interactive learning activities encourages a deep approach to learning...and enhanced understanding of content" (Kember). Being given the opportunity to provide this type of learning tool that may help others understand secret sharing and homomorphic encryption was one of the driving factors for pursuing this project.