Finite field inversion method based on hardware design and device thereof

Abstract

The invention discloses a finite field inversion method based on hardware design, which is applicable to an elliptical curve encrypt system. The method comprises the following steps: using a monadic polynomial in a finite field GF(p) as an input element a and defining an irreducible polynomial f(x), wherein a=am-1x+am-2x+to +a1x+a0, f(x)x=+fm-1xx+to +f(1)+f(0), ai and fi are respectively the coefficients of the input element a and the irreducible polynomial f(x); the input element a being repeatedly multiplied or divided by x and adding the results, and outputting the multiplicative inverse a of the input element a. Correspondingly, the invention further provides a finite field GF(2) inversion device based on the hardware design, therefore, the invention ensures rapider calculation speed, thereby greatly improving inversion operating efficiency. In addition, the working frequency of the inversion device is close to that of other operation devices in the encrypt system so as to fully improve the hardware source utilization rate of the inversion device.

Description

technical field [0001] The invention relates to elliptic curve encryption technology, in particular to a method and device for inverting a finite field based on hardware design in an elliptic curve encryption system. Background technique [0002] Elliptic Curve Cryptography (Elliptic Curve Cryptography, ECC) was proposed by Victor Miller and Neal Koblitz in 1985. Its advantage is that it provides the same security as other cryptosystems and has a smaller key size, so it is currently known It is a public key system that can provide the highest bit strength among all public key cryptosystems in the world. Smaller key size means reduced memory requirements and reduced computing time, especially suitable for low power consumption and high-speed encrypted security applications, such as smart cards, personal computer memory cards, or any other types of handheld or portable devices application. The public key encryption algorithm standard P1363 established by IEEE (Institute of E...

AI Technical Summary

Problems solved by technology

However, with the increasing development of cryptography applications, in the application of some high-speed and low-power electronic devices, such as smart cards, personal computer memory cards, or any other handheld or portable devices, such algorithms still limit the processing of the entire system. Capacity and Power Consumption

[0008] In summary, the existing finite field inversion scheme applied to the elliptic curve encryption system obviously has inconvenience and defects in actual use, so it is necessary to improve it

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