Improved known plaintexts attack on Domingo-Ferrer homomorphic cryptosystem

Abstract

This paper is devoted to known plaintexts cryptanalysis of homomorphic cryptosystem proposed by Domingo-Ferrer. In previous works it was shown that at least pairs (plaintext, ciphertext) are necessary to recover secret key, where is a degree of polynomials representing ciphertexts. Here we analyze existing known plaintext attack. And also slightly modified attack on this cryptosystem is presented. It allows to reduce the necessary number of pairs meaningfully. In particular interception only of two pairs may be enough for successful key recovering with overwhelming probability. The running time of our attack depends polynomially on and logarithmically on plaintexts space size as well as for previous attack. We provide the results of computer experiments.

Keywords

• атака по известным открытым текстам
• гомоморфное шифрование
• облачные вычисления