Homomorphic public-key encryption (ElGamal)
Homomorphic encryption is a public-key encryption scheme with the additional property that it is possible to do computation on encrypted values. The additively homomorphic ElGamal encryption scheme has the property that given two encrypted values under the same public key anyone can compute an encryption of the sum of these messages. This addition requires no knowledge of the private key. This property can be used to manipulate encrypted account balances in order to process transactions.