Homomorphic encryption is a cryptographic method that allows mathematical operations on data to be carried out on cipher text, instead of on the actual data itself. The cipher text is a encrypted version of the input data (also called plain text). It is operated on and then decrypted to obtain the desired output. (Chumbley)

Click one of the following links to download a demo of homomorphic number encryption using Shamir's Secret Sharing:


Summary

Each user-provided number is used to create the corresponding encrypted shares. The shares of the second number are then added to or subtracted from the shares of the first number to produce the encrypted results. These results are then passed through the reconstruction function, which utilizes Lagrange Interpolation, to produce the original sum or difference for the user inputs.