The Research Of Dynamic Encrypt Algorithm Based On The Ergodic Matrix

With the rapid development and wide application of communicationtechnology and network technology, more and more information has beentransmitted through the network, the network economy and e-commerce hasgradually entered our society, and touches every corner of modern economicfield. But faced with numerous serious threats to the network informationsystem, the security and confidentiality of the information are becomingincreasingly important, and the technology based on cryptography is the coreof information security and confidentiality. The cryptography is playing anirreplaceable important role in authentication system and digital signatures. Itis often compared to a computer network information superhighway, thencryptography is the information superhighway management systems, andonly under the management of cryptography, the operation of data is mostsafe. All above makes the cryptography and technology an important researchfield. With the application and perfection of the traditional cryptography,several new branches in this field bring up, such as chaotic cryptography andquanta cryptography and so on. In recent years, the burst of computerhardware has a great impact on cryptograph. Therefore, researching andimproving the encryption algorithm has significant meanings. The mainpurpose of this dissertation is to design a new encrypt-method ——dynamicencrypt algorithm based on ergodic matrix.Dynamic encrypt algorithm, which is based on the idea of encryptionusing the dynamic algorithm, is an algorithm that can generate algorithm inrandom. It can promise the algorithm changing each time we use it, so thatthe security of our algorithm is not only depend on the protection of the key,but also the protection of the algorithm. Its theory is not same to the one oftraditional cryptography, chaotic cryptography and quanta cryptography at all.Dynamic encrypt algorithm, whose length of the key is unconfined, issuitable to encrypt information with any length. The time cost of encryptionis low, and the system is more secure (it can be strengthen further), so it haspromising prospect.The basic idea of dynamic encrypt algorithm is choosing a proper size ofalgorithm space CS according to the key from an algorithm space ASapproaching infinity, and then choose algorithm in space CS in Real-Random.The cryptanalysts knows AS, but with no knowledge about the key, he cannot get CS,and using exhaustive method to get algorithm is impractical,moreover, the key is unknown, so it is very difficult to get any informationabout the algorithm and the key.In this paper, we constructs dynamic encrypt algorithm based on theergodic matrix over finite field, the number of which is large. The ergodicmatrix has a satisfactory ergodic property, and it is reversible, so it can beused for encryption conveniently (Chapter 3 in details). In order to get theinstruction set ,we choose suitable size space from the infinite ergodic matrixspace, and get Ergodic Matrix Set from the space chosen according to the key,then choose ergodic matrix in real-random from Ergodic Matrix Set. TheInstruction Set can be generated by the ergodic matrix chosen. The process ofdynamic encryption is using the instruction in the Instruction Set according toa certain sequence and rule to encrypt information。In this dissertation, we put forward dynamic encrypt algorithm A thatsuitable for encrypting information of short length and dynamic encryptalgorithm B that suitable for encrypting information of long lengthrespectively. Dynamic encrypt algorithm A can be described in brief asfollows:1. We initiate pseudo-randomizer using system clock, and mix thecertain length of real-random sequence generated by pseudo-randomizer withthe plaintext(do XOR operation), then connect the real-random sequence tothe behind of the result, we get the preprocessed plaintext。2. Generate the Ergodic Matrix Set of given size according to the key.3. Choose ergodic matrix to construct Instruction Set from ErgodicMatrix Set according to the preprocessed plaintext, and divide the plaintextinto blocks according to the size of the instructions.4. Encrypt the divided plaintext using the instructions in the InstructionSet, each instruction is used to encrypt a block of the plaintext。Dynamic encrypt algorithm B can be described in brief as follows:1. We initiate pseudo-randomizer using system clock, and mix thecertain length of real-random sequence generated by pseudo-randomizer withthe plaintext(do XOR operation), then connect the real-random sequence tothe behind of the result, we get the preprocessed plaintext。2. Use static Ergodic Matrix Set, and choose ergodic matrix to generatethe Instruction Set according to the key.3. Connect the head and the tail of preprocessed plaintext, which isregarded as a ring, and decide the start position of the first ring, the length ofthe change between each ring and the times of ring N according to the keyand the length of plaintext.4. Choose instruction from the Instruction Set in sequence, and dividethe plaintext into blocks according to the instruction. Choose a bit in randomfrom the last block of the plaintext to decide the changing rule to theinstruction of this ring, and change the instruction of this ring according tothis rule.5. Encrypt the plaintext using the changed instruction, don't encrypt thelast block. Encryption of this ring is over.6. Move the start position of encryption behind the given length, andthen turn to 4, do it in circle N times, then the encryption is over.A lot of experiment and the statistic data shows that the result encryptedusing algorithm A and B are all Real-Random, and there are not statistic rule,although encrypting the same plaintext several times, the result has not directrelation. The rate of encryption and decryption is very quick, especiallyalgorithm B, which is because the static ergodic matrix set is used, and thetime cost of both encryption and decryption is even lower. In this paper, weanalyze the ability of the dynamic encrypt algorithm to resist attack accordingto the most popular way of attract. From the result, we can see that theseattract way is not feasible for dynamic encrypt algorithm based on theergodic matrix over finite field.As for the advantage of the dynamic algorithm, in the last chapter of thisdissertation, we put forward a practical way to using the dynamic encryptalgorithm in digital signature,authentication and so on, the more widelyapplication is depend on the study further. We firmly believe that thedynamic encrypt algorithm in this dissertation must have more application.