Electronic Scoring Scheme Based on Real Paillier Encryption Algorithms

Paillier algorithm has higher time efficiency than other homomorphic encryption algorithms due to only one power operation is required, but its encryption range is limited to integer, which cannot meet the need of electronic scoring system to encrypt real. To solve the problem, an electronic scoring scheme based on real Paillier algorithm is put forward. In the proposed scheme, compound transformation is introduced to convert real to large integer. The encryption range of Paillier algorithm is extended from integer to real by the large integer operation, which can make the scoring results more precision. In addition, a more secure and efficient two-way identity authentication strategy between clients and servers is designed by using Horner's rule. After hashing the username and password by Horner's rule, the obtained hash value is encrypted and transmitted, which can not only improve system security by avoiding disclosure of user's information during transmission, but also increase the computation efficiency due to the reduction of data size in encryption and decryption. In the experiment, compared with the existing encryption algorithms on different scoring data sets, the whole encryption and decryption time is slightly increased by 0.28% compared with the traditional Paillier, but computing real score is realized in the proposed method. The efficiency of addition and multiplication of the proposed method is increased averagely by 25.99% and 42.75%. The average shorten time of two-way identity authentication is 27.22 milliseconds due to the using of Horner's rule. When the number of clients is more than 105, the time efficiency is improved more obviously.