Ciphertexts-only attack on a linear fully homomorphic cryptosystem

The paper proposes a new ciphertexts-only attack on a linear fully homomorphic cryptosystem based on the problem of big numbers factorization. Theoretical and practical estimations of probability to find a key using this attack are given. Also, a link between factorization problem and cryptosystem security is analysed. It is shown how to increase the efficiency by replacing modulo $n$ without loss of cipher strength.