Introduction to Homomorphic Encryption and Schemes

Abstract

Homomorphic encryption (HE) enables processing encrypted data without decrypting it. This technology can be used, for example, to allow a public cloud to operate on secret data without the cloud learning anything about the data. Simply encrypt the secret data with homomorphic encryption before sending it to the cloud, have the cloud process the encrypted data and return the encrypted result, and finally decrypt the encrypted result. Here is a simplistic “hello world” example using homomorphic encryption:

# Every encryption needs a secret key. Let's get one of those. myEncryptionKey = generateEncryptionKey() # Now we can encrypt some very secret data. encrypted5 = encrypt(myEncryptionKey, 5) encrypted12 = encrypt(myEncryptionKey, 12) excrypted2 = encrypt(myEncryptionKey, 2) # We have three ciphertexts now. # We want the sum of the first two. # Luckily we used homomorphic encryption, so we can actually do this. encrypted17 = addCiphertexts(encrypted5, encrypted12) # Maybe we want to multiply the result by the 3rd ciphertext. encrypted34 = multiplyCiphertexts(encrypted17, encrypted2) # See that? We operated on ciphertexts without needing the key. # But no matter what we compute, the result is always encrypted. # To actually see the final result, we have to use the key. decrypted34 = decrypt(myEncryptionKey, encrypted34) print(decrypted34) # This should print '34'