Cryptanalysis of a Public-key Scheme Based on the Chinese Remainder Theorem

A heuristic attack against a fast public-key scheme is put forward,which is based on the Chinese remainder theorem.A basis of lattice L is constructed using the public-key and a target vector t using the ciphertext,then the plaintext is a lattice vector close to t.By Kannan's embedding technique,a new lattice L₁ is designed from lattice L,and the plaintext will be a short vector of lattice L₁.As the dimensions of L and L₁ are 6 and 7,respectively,the attacker can compute the two vectors by invoking the Lenstra-Lestra-Lovasz(LLL) algorithm in practice and then obtain the plaintext.Experimental results show that the attack is validated.