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1. The Polynomial - Basis Multiplier in the finite field is the key module to realizing ECC basic operations.

2. The finite field arithmetic is the base of cryptography and inversion is the kernel arithmetic operation.

3. Firstly, correlation immune functions over finite field is discussed, the relationship among correlation immune, statistical independence and balance is revealed.

4. Multiplication operation over the finite field is the most crucial part in the elliptic curve cryptosystems.

5. The presentation of the finite field elements in WDB is studied. And based on the computing method for the optimum WDB, the design for the bit parallel multiplier of finite field is presented.

6. A method of zero-knowledge identity verification is discussed here, and the specified. scheme is put forward based on the encryption properties of the ergodic matrices over the finite field.

7. A new definition of linear spectrum of multi - valued logical functions over finite field was proposed.

8. Secondly, one construction of Cartesian authentication code from norm form of one class of nilpotent matrices over finite field is presented and its size parameters are computed.

9. This paper , firstly introduces the elliptic curve in finite field and algebraic law of its point group, gives the order of the group.

10. There are two applications to the RB. One is array processing and the other is quaternion finite field transform.

11. Hardware implementation for the all - erasure RS decoder is proposed, including the finite field arithmetic operation units.

12. This paper gives some properties of companion matrix of polynomial over finite field with its application for evaluating period of linear shift register sequence and minimal length of cyclic code.

13. A new high regular structure of partial parallel multiplier for irreducible trinomial generated finite field is proposed.

14. A Characteristic polynomial algorithm for computation of Chebyshev polynomial over finite field is modified to achieve faster execution speed.

15. We got the standard form of nonsingular matrix over the finite field by means of BN pair decomposition under the similarity transformation of the permutation matrix.

16. Two methods considering dynamic water pressure in ANSYS were studied,(Sentencedict) which were finite field addition mass method and sequence weak coupling solving method.

17. In this thesis, the design and FPGA implementation result of a finite field polynomial multiplier is presented, whose arithmetic architecture is based on the number theoretic transform.

18. The first is establishing artificial boundary problem, because of simulating the infinite field from the finite field in which intercept from the infinite field, so we introduce artificial boundary.

19. In this paper, enumeration problems in the orthogonal geometry over a finite field with characteristic 2 are studied, and an enumeration theorem is proved.