Homomorphic encryption is a form of encryption which allows specific types of computations to be carried out on ciphertext and obtain an encrypted result which is the ciphertext of the result of operations performed on the plaintext. For instance, one person could add two encrypted numbers and then another person could decrypt the result, without either of them being able to find the value of the individual numbers. Homomorphic encryption schemes are malleable by design. The homomorphic property of various cryptosystems can be used to create secure voting systems, collision-resistant hash functions, private information retrieval schemes and enable widespread use of cloud computing by ensuring the confidentiality of processed data.
There are several efficient, partially homomorphic cryptosystems, and two fully homomorphic, but less efficient cryptosystems. Although a cryptosystem which is unintentionally homomorphic can be subject to attacks on this basis, if treated carefully homomorphism can also be used to perform computations securely.
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... Each of the examples listed above allows homomorphic computation of only one operation (either addition or multiplication) on plaintexts ... structure of the plaintexts) is known as fully homomorphic encryption (FHE) and is far more powerful ... allowing the construction of programs which may be run on encryptions of their inputs to produce an encryption of their output ...