|Title||A fully homomorphic cryptosystem with approximate perfect secrecy.|
|Author(s)|| Michal Hojsik, Veronika Pr ulpanova|
|Type||Book, Chapter in Book, Conference Proceeding|
|Abstract||We propose a new fully homomorphic cryptosystem called Symmetric Polly Cracker (SymPC) and we prove its security in the information theoretical settings. Namely, we prove that SymPC approaches perfect secrecy in bounded CPA model as its security parameter grows (which we call approximate perfect secrecy).|
In our construction, we use a Gröbner basis to generate a polynomial factor ring of ciphertexts and use the underlying field as the plaintext space. The Gröbner basis equips the ciphertext factor ring with a multiplicative structure that is easily algorithmized, thus providing an environment for a fully homomorphic cryptosystem.
|Keywords||Polly Cracker, Fully homomorphic encryption, Gröbner bases|