Automated Design Of The Cipher Components

With the penetration of computer and Internet, the door to the network and information age is opening. The computer network security and information security have become the critical issues, so a variety of methods is been used to enhance information security. The most effective and simple way to ensure information security is the use of cryptography. And the cryptography is one of the key information security technologies. For the block ciphers, there are two commonly structures that are the SP structure and the Feistel structure, this thesis has discussed the design of block ciphers with the both structures. To design the cipher with these two structures, it first breaks the cryptosystem down into the cipher components of the design, second generates the each cipher component that has good cryptographic characteristic, viz. resistance to the existing attacks, finally assembles these cipher components into a round function through the whole test and can get the cryptosystem carrying out multi-Rounds encryption. The design method in this thesis can also be generalized to other structures of the cryptosystem. In the cryptosystem with Feistel structure or SP structure, the cipher components to design is classified two categories, one class is non-linear components called S-box from the confusion effect, another class is linear components called the P-replacement from the diffusion effect. We have given comprehensive discussion of the S-box on several cryptographic properties, including the nonlinearity, the differential uniformity, the diffusibility, the correlation immunity and the avalanche criteria, these cryptographic characteristics need to be considered in the design of the cipher. The design of the S-box mainly thinks out the nonlinearity, the differential uniformity and algebraic attack in this thesis. The cipher design and cryptanalysis are always mutual promotion and common development, and the cryptanalysis methods today constantly heighten and technologies constantly improve, so we must have given an integrated, comprehensive consideration about the application of various attack methods in order to resist effectively to linear attack, differential attack and algebraic attacks, which are today’s mainstream analysis way. In order to design the security cryptosystem, we have studied the automated design of the cipher components including the following questions.The first major content to research is orthomorphism, which is used to design cipher components because of its unique cryptographic properties. The orthomorphisms are classified into two kinds, one is the linear orthomorphism the other is nonlinear orthomorphism that can be utilized to design the S-box. So this thesis focuses on the nonlinear orthomorphism over the finite field GF(28), which the nonlinear orthomorphism is designed to the S-box that can input 8 bits and output 8 bits. We have summarized the extant generation algorithm of the nonlinear orthomorphism over GF(28), and take mainly advantage of the permutation polynomial and the Boolean permutation to study the nonlinear orthomorphism over the finite field GF(28). The distribution of the orthomorphic permutation polynomial’s degrees is important issue when we are utilized to the permutation polynomials to study the orthomorphism, it is known what degrees of the orthomorphic permutation polynomials exists and what degrees don’t. That the Boolean permutation utilized to study the orthomorphism is convenient and easy to present the nonlinear orthomorphism over GF(28).Since the number of the orthomorphism over GF(28) is a "combinatorial explosion" in comparison with the number of the orthomorphism over GF(24), and it is difficult to fully generate the all orthomorphism over GF(28), we have presented the non-linear orthomorphism over GF(28) combined with evolutionary computation or intelligent algorithm after summing up the generation algorithm of the orthomorphism. This section mainly covers two points:(1) the production of the non-linear orthomorphism over GF(28); (2) the degrees distribution of the orthomorphic permutation polynomial over the finite field GF(28). The second study contents are that have generalized the linear orthomorphism over the finite field. We have studied the generalized linear orthomorphism over the finite field with the arbitrary prime number as the characteristic, and have solved the problem of the structure and count on the generalized linear orthomorphism. At the some time, we have studied the linear orthomorphism (or omni-direction permutation) and the orthomorphic matrix over the general integer residue class ring Zn, and have obtained their construction methods and counting properties. This thesis has completely solved the counting and structural problems of the omni-direction permutation, the linear orthomorphism and the orthomorphic matrix over the ring. Finally, the generalized linear orthomorphism is used to design the P-permutation, because the linear orthomorphisms only have the maximum branch number 5 over the finite field with the characteristic 2, when the order of the linear orthomorphism is less than or equal to 8.The third research contents are that the error-correcting code is used to design the P-permutation in this thesis. We have mainly designed the P-permutation used on the Goppa code and the BCH code, which have the advantage that the branch number is more than the desired lower bound and the shortcomings that its branch number difficultly arrive at the maximum value until the special circumstances. We have studied the circulant matrices over the finite field in this section because it has been utilized in AES, and we have obtained the methods about the judgment criterion of reversible matrices and the calculation of inverse matrices. Also we have discussed some properties of the circulant symmetry matrices and the circulant orthomorphic matrices. We have presented the generation algorithm of circulant matrices of the order 4 with the maximum branch number.The last part is that has studied the theory and the application scopes in the cryptograhy about the evolutionary computation, the particle swarm optimization and the ant colony algorithm. We have generated the nonlinear orthomorphisms over the finite field GF(28) from the orthomorphisms over the finite field GF(24) based on the evolutionary computation and the particle swarm optimization algorithm. We demand the S-box from the design of the orthomorphisms to satisfy that the nonlinearity is as large as possible, the differential uniformity is as small as possible and also the algebraic attack is resisted. This thesis has pointed out that the multi-round characteristic and the linear approximation hull probability can be searched by the ant colony algorithm in the multi-round cryptosystem, which can bring advantage to the whole cryptosystem resisted the linear and differential cryptanalysis. The orthomorphisms over GF(28) relied on the Evolutionary Computation and particle swarm optimization algorithm to generate have been transformed into the orthomorphic permutation polynomials, which is advantaged to study the degree’s distribution of the permutation polynomial.