| With the improvement of computing capability, the security of cipher has been queried extensively. It is urgent to study how to enhance cipher (especially block cipher) security intensity. This study has some academic value and application prospect.Main work and innovations in this thesis are as follows:1. An excellent lower bound of orthomorphism over Galois field GF(2") was derived. Enumerations and counting of orthomorphism is one of the research hotspot in the study of orthomorphism. Based on the construction of Latin Square transversal, an excellent lower bound of orthomorphism was derived. It shows the existence and plentifulness of orthomorphism over GF(2").2. A novel model of recurrent transposition and mapping was proposed in this thesis, to guarantee the security of classical block ciphers. It was named as Grow Tree (G-T). G-T could be used in cryptography to improve data security. The clue of G-T is: consider each data block as the coefficient matrix for orthogonal basis in lower dimensional space. Map the coefficient matrix in lower dimensional space to higher dimensional space.3. It was proposed in this thesis a class of G-T based on crossover operator, mutation operator in genetic algorithm and wavelet transform. Ie. Forward G-T transform should transfer data by operator Fk and the inverse wavelet transformation. Experiments and analysis show the improvement of data security.4. It was proposed in this thesis another grow tree based on orthomorphism and finite filed wavelet-FW-GT, to improve G-T's computation speed and security intensity. Based on orthomorphism, perators Fk has the merits of low computational complexity and high security intensity. Based on binary filed wavelet transform, peratorφdiscarded the problem of high computational complexity. Experiments show when input data is above 32k, the operation time of FW-GT is only half of G-T. Using FW-GT to transfer data before coding, could improve data anti-attack ability, and improve data security intensity.
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