Research, Probability-based Public Key Cryptosystem

Before 1984, S. Goldwasser and S. Macali proposed probability public-key cryptography(PPC), all public-key cryptosystems have all sorts of shortages for their certainty. Because public-key cyrptosystem uses trapdoor one-way function f(x),the possibility of calculate x or some part information of x from f(x) can not be excluded. However, PPC encrypto per bit of plaintexts, so it can overcome the shortage of certain public-key cryptosystem. However, probability cryptosystem is not perfect, a lot of research finds that the system has the shortages such as too large expansion rate, unable signature and easy to be attacked.Base on above background, this paper does some research on probability cryptosystem.The first part of this paper introduces the development of cryptologic technique, the constitute of cryptosystem and the theory of digital signature. It also introduces the background and significance of PPC, sorts of common PPC and its mathematical base.The second part builds a safe and high effective RSA based PPC by the one-way character of trapdoor function. The improved algorithm maintains security of old one, and reduces expansion rate of ciphertexts. What's more, this paper builds a digital signature scheme, and analyses the security of new algorithm and digital signature scheme.The third part studies PPC which proposed by Pallier-Pointcheval in 1999, without lowering the security, this part improved a one-way trapdoor permutation with characters of composite residuosity class. The efficiency of encrytion and decryption is improved through comparison. The digital signature which is obtained from improved algorithm are RSA[n,n] security as well as the new scheme.The forth part analyses an algorithm like Xn=sin2(θπzn). A new chaos map is proposed which can solve the problems the old one has. Changes the multiple to square of the first iteration function, then it can resist the attack of continued fractions, this new algorithm improves its statistical quality through changing another iteration function. The random series which the new algorithm generates is tested with Golomb random hypothesis.The last part discusses the conclusion and perspective of PPC.