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Implementation method and system of sm2 encryption, signature and key exchange based on efficient modular multiplication

A technology of key exchange and implementation method, applied in the field of SM2 series algorithm implementation methods and systems, can solve problems such as low computational efficiency, and achieve the effect of resisting SPA analysis

Active Publication Date: 2022-03-22
SHANGHAI JIAO TONG UNIV
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Problems solved by technology

For the choice of coordinate system, there are usually projective coordinates and Jacobian coordinates. These two coordinates can avoid a large number of inversions, but after the scalar multiplication calculation is completed, the resulting coordinates need to be converted to affine coordinates. Therefore, in the entire calculation The process requires an inversion, resulting in low computational efficiency

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  • Implementation method and system of sm2 encryption, signature and key exchange based on efficient modular multiplication
  • Implementation method and system of sm2 encryption, signature and key exchange based on efficient modular multiplication

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Embodiment 1

[0028] Such as figure 2 As shown, the present embodiment relates to the system that realizes the implementation method of SM2 encryption, signature and key exchange based on modular multiplication, including: prime number multiplication module, Montgomery modular multiplication module, modular inverse module, scalar multiplication realization module, wherein: prime number multiplication The module converts the multiplication operation involving SM2 prime numbers into shift and subtraction operations. The Montgomery modular multiplication module updates the calculation efficiency of the shift and subtraction operations according to the prime number characteristics and generates a fast realization of prime number multiplication and outputs it to the modular inverse module. The modular inverse module Carry out the modular inverse operation and generate a complete and efficient modular multiplication implementation and output it to the scalar multiplication implementation module. ...

Embodiment 2

[0035] This embodiment relates to an optimized key pair generation scheme for a digital currency hardware wallet, specifically comprising the following steps

[0036] Step 1. The user adds the seed of the key generation algorithm in the digital currency hardware wallet.

[0037] Step 2. Use the key derivation algorithm to generate the user public key as the user account address, and generate the user private key for signing the blockchain information based on the public key and the Montgomery Modular Multiplication method optimized for the prime number feature.

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Abstract

A method and system for realizing SM2 encryption, signature and key exchange based on efficient modular multiplication. According to the optimized Montgomery Modular Multiplication method based on the characteristics of prime numbers, the multiplication operation involving SM2 prime numbers is optimized, and then the modular inverse operation is performed, and finally SM2 is realized. Fast implementation of scalar multiplication operations in signature, encryption and decryption, and key exchange. The present invention utilizes the characteristics of SM2 prime numbers to realize efficient modular multiplication, constructs efficient scalar multiplication realization and modular inverse realization based on the modular multiplication, and is applicable to the specific realization of signature, encryption and decryption and key exchange algorithms in SM2.

Description

technical field [0001] The present invention relates to a technology in the field of computer security, specifically a modular multiplication implementation based on the prime number feature whose efficiency is twice that of the traditional implementation. Implementation method and system. Background technique [0002] Scalar multiplication is the basis for the security of SM2 (elliptic curve public key cryptography) and even all ECC schemes. The existing SM2 based on elliptic curves includes three schemes: signature scheme, key exchange scheme and encryption and decryption scheme, and among the three schemes The most computationally expensive part is the scalar multiplication operation. Since SM2 is defined on the field of prime numbers, affine coordinates cannot be used in implementation. For the choice of coordinate system, there are usually projective coordinates and Jacobian coordinates. These two coordinates can avoid a large number of inversions, but after the scala...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F21/60G06F21/64
CPCG06F21/602G06F21/64
Inventor 许森谷大武郁昱陆海宁
Owner SHANGHAI JIAO TONG UNIV
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