The Construction And Application Of Cryptosystem Based On Satisfiable Problem

With the rapid development of information technology,the security issue of users' information in the transmission process under the big data environment has become one of the hot spots that people are most concerned about.As we all know,the public key cryptosystem is an important research content of modern cryptography,and it is also an important tool to protect the security of user data in the big data environment.However,many classical public-key cryptosystems cannot satisfy the higher provable security,and many existing public-key cryptosystems are often designed to satisfy certain special properties(like homomorphism,verifiability,delegation,etc.),and it is difficult to achieve higher security,so it is particularly necessary to research how to construct a secure public key encryption system.This paper based on the satisfiability problem(SAT)and taken the SRR model and provable security theory as the tools to studies the security of public key cryptographic schemes based on random regular satisfiability problems.The main research works of this article are as follows:(1)A public key encryption scheme based on satisfiability problem.First of all,the traditional SRR model is improved to satisfy the function of data encryption.Secondly,according to the existing research on the critical value of random regular(k,s)-SAT problems,constraining reasonably constraint density of the constructed (3,s)-SATconjunctive normal form to generate difficult instances and encrypting the plaintext.Finally,it is proved under the framework of provable security theory that this scheme can securely against chosen-plaintext attack.(2)A hybrid encryption scheme based on satisfiability problem.Firstly,based on the difficulty problem of the random regular formula near the phase transition point,combining and improving the SRR model to encrypt the plaintext.Secondly,basedon the existing Damg?rd Elgamal scheme,introducing the data encapsulation mechanism and the hash function to improve its security,and a hybrid encryption scheme based on SAT and discrete logarithm problem is proposed.Finally,the analysis shows that compared with the existing SAT-based hybrid encryption scheme,this scheme has a shorter private key length,satisfies ciphertext verifiability,and can securely against adaptive chosen-ciphertext attack.(3)The application of hybrid encryption scheme based on satisfiability problem for confidential express sheet.Using the SAT-based hybrid encryption algorithm to encrypt users' information,in the stage of express transportation and dispatching,due to the ciphertext verifiability and algorithm security,not only can protect the privacy of users' information when the express transported below the line,but also protect the integrity and availability of information so that reduces the risk of leakage of user information online.