Analysis And Implementation Of Efficient Calculation Based On Bilinear Pairing

Public Key Cryptosystems is one of the most key technology to achieve information security. The efficiency of implementations in cryptosystems is one of the hottest aspects in cryptography. Modifying and optimizing different algorithms is common approach to achieve efficiency. Scalar multiplication and multiple scalar multiplications are the most crucial algorithm in Elliptic Curve Cryptosystems (ECC). The calculation of elliptic curve in Tate Pairing is the core operation of Identity-Based Cryptosystems.In this dissertation, our main work focuses on the following aspects: First, we introduce the elliptic curve scalar multiplication algorithm, including binary method, NAF method and window method. And we improve the NAF window method algorithm. This improved algorithm is more efficient than the original algorithm by about 3.4%; Then, we describe the original algorithm Shamir and JSF algorithm. Meanwhile, we propose a novel figure split algorithm inspired by JFK algorithm. In addition, we expend this algorithm into the implemetation of the tree shape algorithm. Experimental results show that our algorithm can improve the efficiency over 50% than original fixed-point scalar multiplication. Finally, we implement our identity-based encryption algorithm exploiting Maical Library. The application of the program is enhance our understanding of elliptic curve cryptosystem. By a few modifications, the program can be used in business as a encrypt software.