SM2 elliptic curve signature verification algorithm

Abstract

The invention discloses an SM2 elliptic curve signature verification algorithm. The SM2 elliptic curve signature verification algorithm comprises the following steps: a digital signature generation algorithm: inputting the original data of a signature party A, comprising system parameters (base point G, order n) of an elliptic curve, a hash value ZA, a private key dA of the signature party A and amessage M to be signed; and obtaining a random bit string W. In a process of generating a digital signature, a segment of random bit string is obtained at first, then after an XOR operation is performed on the message to be signed and the random bit string, a NAND operation is performed with the hash value, if the signature information is intercepted by a lawbreaker in a transmission process, thelawbreaker cannot completely crack or counterfeit the signature information without knowing the XOR operation and the NAND operation in the signature process, thereby improving the security of the signature information and preventing the lawbreaker from cracking and counterfeiting the signature information after intercepting the signature information.

Description

technical field [0001] The invention relates to the technical field of information security, in particular to an SM2 elliptic curve signature verification algorithm. Background technique [0002] Identity authentication technology is the leading force to ensure information security, and the design and implementation of authentication system is very important. Only through a high-reliability identity authentication system can the information security of both parties in communication be effectively guaranteed, and information can be prevented from being intercepted by criminals during transmission. SM2 is an elliptic curve public key cryptographic algorithm released by the State Cryptography Administration on December 17, 2010. Digital signature technology is an important application of the elliptic curve public key cryptographic algorithm. It plays an important role in modern e-commerce and government affairs. It can ensure the integrity of the message during transmission, a...

AI Technical Summary

Problems solved by technology

[0003] During the signature generation (signature verification) process of the existing SM2 signature verification algorithm, most of the messages to be signed (the message to be verified) and the hash value are directly spliced ​​at the beginning and the end. attack, low security

[0004] In the operation process of the SM2 elliptic curve public key cryptographic algorithm, the most time-consuming is the point multiplication algorithm, and in the point multiplication operation, the most time-consuming is the modular inverse operation, which takes more than ten times the time required for the modular multiplication operation. The number of modular inversion operations required to complete a point multiplication operation under different coordinates is different. In the Montgomery point multiplication algorithm under the affine coordinate system, each point operation (point addition, point doubling operation) needs to be performed One modular inverse operation, multiple modular inverse operations will consume a lot of time. In the Montgomery point multiplication algorithm under the standard projected coordinates, point operations (point addition, doubling point operations) do not need to perform modular inverse operations, but the modular multiplication operation The number of times will be greatly increased, and it will also consume a lot of time

The traditional Montgomery point multiplication algorithm often only performs point multiplication operations in one coordinate system, uses only one modular multiplication unit and adopts a serial calculation method, resulting in slower point multiplication operations, which in turn leads to slower operation speeds in the entire signature verification process. slow, time consuming problem

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