Probabilistic Cryptosystem Based On Public Key Encryption

There are two problems discussed in this paper. One is the probabilistic cryptosystem based on the RSA cryptosystem, and the other one is an improved scheme of BG probabilistic cryptosystem.In the first part, the paper analyzed that the public-key cryptography can achieve digital signatures. However, the public-key cryptography uses the method of block encryption. When the cipher texts have special forms, it is possible to compute all or some information about the plain texts from the cipher texts. So it can’t guarantee the security of every bit. This defect drew us attention to the probabilistic cryptosystem. The probabilistic cryptosystem encrypts the plaintext bit by bit. It can ensure the security of every bit. But it can’t achieve digital signature, that is, the receiver can’t decide the source of the messages. Because of the advantages and disadvantages of these two cryptosystems, using the one-way property of trapdoor function, without reducing the safety of original function, we presented the probabilistic cryptosystem based on public key cryptosystem which both ensured the security of every bit of the encrypted message, and achieved the goal of digital signature. The paper also shows the encryption program of computer.This article also raised an improved scheme of BG probabilistic cryptosystem based on the theory of quadratic residue and the conversion between decimal and hexadecimal. Firstly, we dealt with sm+1in the cipher text according to the theory of quadratic residue, and then converted Sm+1to hexadecimal. The length of the decimal number is at least2bits longer than the corresponding hexadecimal number when sending a decimal number of the length that is greater or equal to17bits. So, it reduced the data expansion from1+k/m tol+(k-2)/m, which is much lower. These operations didn’t affect the legitimate receiver to recover the plain texts.