VLSI Design Method Of Elliptic Curve Cryptography Based On Prime-field

The point multiplication operation is the core of elliptic curve public key cryptography, this paper mainly pay attention to the point-multiplication over elliptic curves based on prime field, the main work is as follow:This paper optimizes an algorithm which is proposed on one document. Compared with the original algorithm, the improved algorithm reduces two comparison operations, two subtraction operations and one shift operation. Based on the improved algorithm, this paper gives different implementation of 256 bit modular multiplier according to the different design of adder or subtractor in the circuit.Based on a improved extended Euclidean algorithm, this paper designs hardware structure of modular inverse circuit. This algorithm converts the original and complex modulo operation to addition, subtraction and shift operation, uses one subtraction instead of one comparison and subtraction. The circuit can also realize modulo division. According to the three computation structure, the point multiplication circuit is divided into three modules: top module, point-add and double-point module, basic arithmetic module. The algorithm of top module which is used to design the circuit structure is an improved binary algorithm.The development platform is VirtexII PRO XC2VP30, this chip is produced by Xilinx, the EDA software is ISE 9.1. The test result shows, when the data's length reaches 256 bit, the highest frequency of the point multiplication circuit can reach 71.426 MHz, and power reaches 685 Mw, the design used 13940 Slices and 5433 Flip Flops. The assessment report shows the design has a great advantage in the case of performance, speed and resource consumption.