Research On Public Key Cryptography Scheme Based On Lattice Theory

The status and role of information in society are more and more important.Theinformation has become an important strategic resource for the development of oursociety. So information security has got people’s widely spread attention. Public keycryptography has become the core of information security technology in today’ssociety by its strong characteristic, many researchers devote to the study of publickey cryptosystem. RSA and knapsack public key cryptosystem scheme because ofencryption and decryption fast, convenient and practical characteristics are widelyused in our real life. In order to ensure that the proposed scheme can be safely usedin practice, the safety analysis of the application for these programs become moreand more important and practical.There are many methods of cryptanalysis, latticereduction is one of them, it is an important tool. In cryptography applications, someanalysis of cryptographic schemes can be ultimately equivalent to lattice reductionproblems. The paper will research on the security around the RSA and the knapsackpublic key cryptosystem, by the lattice in the analysis method of security analysis,the main research contents include:(1) The security analysis of an improved algorithm of RSA through thelattice code.Recently, the improvement of RSA method is in an endless stream.Thispaper will attack a new improved RSA algorithm based on the idea of thelattice, through the different parameters of the experiment, according to theLLL algorithm.Based on the analysis of the experimental results, we can directlybreak it or get some plaintext of it, so this improved algorithm is security vulnerability, also needs to be further improved.(2) The security analysis of a knapsack cryptosystem algorithm throughthe lattice code.Knapsack public key cryptosystem can encryption quickly, it has a strongpracticability, and itself is based on knapsack problem (NP completeness)characteristics of the problem, so it is widely applied to many resources restricted thereality of the environment, such as memory is limited; time is limited, and so on. Therefore, analyzing the security of the knapsack public key cryptosystem isparticularly important. In this paper,we will use the current popular ideas of latticecode to do an attack experiment, under the different parameters of a new scheme ofbackpack password, which shows that the improved algorithm still exist securitythreat, also doesn’t fit into the practical application.According to the research content classification, the contribution and innovationof this paper include:(1) To deepen the code analysis tool of the lattice theory in the role ofpublic key password security analysis.At present, some scholars have already begun using lattice theory as the codeanalysis tool, but it is not very common. In this paper, we attacked two new publickey cryptography schemes by using the method of lattice code, deepen the theoryplays an important part in cryptanalysis.(2) For two kinds of public-key cryptography algorithm is put forward bythe new statute attacking experiment.By constructing a suitable case, we attacked the two new public key cipheralgorithm for different parameters, detailed the attack experiment of lattice structurescheme and the realization of the pseudo code in the computer.