A Study Of Safety Analysis And Improvement Based On Fast Public Key Cryptosystems

With the development of computer network technology, computer networks andinformation security issues are also increasingly prominent. Whether e-commercedevelopment or personal information and communications, information data and codein the transmission of Internet security needs to be used encryption and decryptiontechnology. At present, the most commonly used password system is designed basedon number theory problem of public key cryptosystems, but with the advent ofquantum computer, its security problem is becoming more and more outstanding, inorder to resist a quantum computer attack, after the era of quantum informationsecurity, to find a quick and efficient encryption scheme is a very meaningful thing.Lattice password system as a typical representative of the public keycryptography scheme of quantum era, on the one hand, its security problem is basedon the grid in the worst case, the attacker in a certain period of time is difficult tocrack, makes the difficult problems in lattice design of choice for public keycryptography. On the other hand, to solve the difficult problems in lattice algorithm isan important analysis tool on the cryptography, has successful analysis or crackedmultiple public key cryptography scheme. Password for grid system design andanalysis in order to pass the research of complex theory, computer has become againstquantum computing core content in the research of theory of public keycryptosystems.In this paper, a kind of public key cryptography scheme, with thought of casebase code on the safety analysis, found that the public key cryptography scheme oflow efficiency, security is not high also. Aiming at these problems, we design a newefficient key scheme, the design and improve fast digital signature scheme, encryptionscheme and so on several aspects has carried on the related research, obtained thefollowing results:(1) In the safety analysis of work: analysis when the random number k is short,use the name LLL algorithm, adopt different parameters of the attack can recover theplaintext cipher; When express length is longer than the other, can be resolvedsuccessfully its private key using Euclidean algorithm, thus the inverse plaintext.Therefore proved by the analysis of the scheme is insecure.(2) In public key cryptography algorithm improvement work: on the premise of not reduce security,a public key cryptography algorithm for the unsafe by using themethod of matrix was improved, make it easy to guarantee difficulty hypothesis(matrix generally constitutes a ring, and there are zero elements, it is difficult toanalyze, encryption faster (more than one can handle); After the plaintext is dividedinto two parts, part of the add2rbytes from the original random K of attack, at thesame time increase the randomness makes the original scheme is more secure. Finally,on the basis of the study puts forward an improved signature algorithm, proves thatthe signature algorithm is safe.