A Point Addition and Point Multiplication Circuit Based on Binary Expansion Field and Its Control Method

Abstract

The invention discloses a point addition and doubling circuit based on binary expansion and a control method thereof. The point addition and doubling circuit includes a finite state machine, a modular multiplication module, a modular square module, a modular addition module, and a modular inverse module, data register, status register, count register and control signal register. By using the finite state machine to call the modular multiplication module, modular square module, modular addition module and modular inverse module, operations such as point addition, point doubling, and coordinate transformation are realized. Since different modules can be called repeatedly, hardware redundancy can be reduced, hardware resources can be fully utilized, and the circuit structure can be simplified, so that the entire circuit consumes fewer clock cycles to work when executing each instruction, and ultimately reduces the time for computing tasks cost, reduce power consumption and heat generation, and increase the battery life of mobile terminals using this point plus and point doubling circuit. The invention is widely used in the technical field of circuits and systems.

Description

technical field [0001] The invention relates to the technical field of circuits and systems, in particular to a point addition and doubling circuit based on binary expansion and a control method thereof. Background technique [0002] In the application of elliptic curve cryptographic algorithm, etc., for the elliptic curve y in the Jacobian weighted projective coordinate system 2 +xyz=x 3 +ax 2 z 2 +bz 6 , asking for P 3 (x 3 ,y 3 ,z 3 ) = P 2 (x 2 ,y 2 ,z 2 )+P 1 (x 1 ,y 1 ,z 1 ), need to go through the following point addition process: [0003] h 3 =h 2 + h 1 , h 6 =h 5 + h 4 , h 7 =z 1 h 3 , h 8 =h 7 the y 2 + h 6 x 2 ,z 3 =h 7 z 2 , h 9 =h 6 +z 3 , [0004] ask for P 3 (x 3 ,y 3 ,z 3 ) = P 1 (x 1 ,y 1 ,z 1 )+P 1 (x 1 ,y 1 ,z 1 ), need to go through the following doubling process: [0005] [0006] It can be seen from the above expressions that both the point addition process and the point doubling process involve...

AI Technical Summary

Problems solved by technology

However, it is not necessary to use the same amount of hardware resources in each round of point addition and doubling calculations, so the existing technology usually causes too much hardware redundancy, and hardware resources cannot be fully utilized. It makes the whole circuit too complicated, and it takes more clock cycles to work, which finally shows that the calculation task takes too long, the power consumption and heat generation of the dot addition and doubling circuits are too large, and it is applied to mobile Disadvantages such as poor battery life at the terminal

Images