Ecc Encryption And Decryption Algorithm Optimization Technology Research And To Achieve

In the cryptographic techniques, in the case of achieving of the same security intensity, the elliptic curve cryptography can be realized by a shorter key. However, with the development of computing power and the appearance of parallel distributed technology, it is possible to brute force cracking in time, so the longer key must be used by us to ensure the information's security. It requires us to optimize the algorithm and to improve speed of the algorithm. In the thesis, the encryption and decryption of the ECC is realized, and the time-consuming operation for the ECC's encryption and decryption is optimized.In the operation of the big integer, by making analyses of the following cases in the thesis, such as the carry, borrow, the addition and subtraction operations to meet non-overflow and multiple-precision is proposed, and the parallel design is made to the multiplication and the point multiplication, and the plain-text embedding is analyzed and realized. The multiplication is the most time-consuming operation of the big integer's operation, so it is necessary to optimize it. In the multiplication operation, a big integer of 2n bits is divided into four n numbers by the high and low, so the speed is improved by the four threads simultaneously computing, each is responsible for the operation of two integers of n bit. By analyzing, the affine coordinates is chose to use. The operation of point addition and multiplying points is realized by using the point addition and multiplying point's formula. The point multiplication is a relative time-consuming operation for the point operation. During the operation, the speed is improved by pre-storing the values of 20P, 21P,…and starting more threads to do the point operation. Due to the particularity of the module in the elliptic curve of prime domain recommended by the NIST, that is mod 4 equals 3, so the deduction is used to completing the plain-text embedding.According to the improved algorithm, the program structure of the ECC in the thesis is designed as follows: the bigger integer ->the point operation -> the parameter set and operation of the ECC's encryption and decryption -> the generation of key -> encryption and the decryption, and the definition and operation of the bigger integer, point and the structure of encryption and decryption are given. The operations of encryption and decryption of the ECC are made based on the bigger integer and the point and the encryption and decryption are completed by the designed program structure. The encryption and decryption of following 4 ECCs, such as 192 bits, 224 bits, 256 bits and 384bis are realized in the thesis.