Abstract: A method for secure comparison of encrypted symbols. According to one embodiment, a user may encrypt two symbols, share the encrypted symbols with an untrusted third party that can compute algorithms on these symbols without access the original data or encryption keys such that the result of running the algorithm on the encrypted data can be decrypted to a result which is equivalent to the result of running the algorithm on the original unencrypted data. In one embodiment the untrusted third party may perform a sequence of operations on the encrypted symbols to produce an encrypted result which, when decrypted by a trusted party, indicates whether the two symbols are the same.

Abstract: A system and method for secure substring search, using fully homomorphic encryption, or somewhat homomorphic encryption. In one embodiment, a first string is homomorphically compared to trial substrings of a second string, each comparison producing a ciphertext containing an encrypted indication of whether the first string matches the trial substrings. These ciphertexts are then combined in a homomorphic logical OR operation to produce a ciphertext which contains an encrypted indication of whether the first string matches any of the trial substrings, i.e., whether the first string is contained in the second string.

Abstract: A method for secure comparison of encrypted symbols. According to one embodiment, a user may encrypt two symbols, share the encrypted symbols with an untrusted third party that can compute algorithms on these symbols without access the original data or encryption keys such that the result of running the algorithm on the encrypted data can be decrypted to a result which is equivalent to the result of running the algorithm on the original unencrypted data. In one embodiment the untrusted third party may perform a sequence of operations on the encrypted symbols to produce an encrypted result which, when decrypted by a trusted party, indicates whether the two symbols are the same.