Publikace na Matematicko-fyzikální fakulta |
2013
Abstrakt
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 Gr¨obner basis to generate a polynomial factor ring of ciphertexts and use the underlying field as the plaintext space. The Gr¨obner basis equips the ciphertext factor ring with a multiplicative structure that is easily algorithmized, thus providing an environment for a fully homomorphic cryptosystem.