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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, which is applied in the field of SM2 series algorithm implementation method and system, which can solve the problem of low calculation efficiency and achieve the effect of resisting SPA analysis

Active Publication Date: 2019-01-04
SHANGHAI JIAO TONG UNIV
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  • Abstract
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  • Claims
  • Application Information

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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

[0029] Such as figure 2 As shown, the present embodiment relates to the realization system that realizes the method described in any one of the above claims, including: a prime number multiplication module, a Montgomery modular multiplication module, a modular inverse module, and a scalar multiplication realization module, wherein: the prime number multiplication module participates in the SM2 prime number Multiplication operations, converted to shifts and subtractions; Montgomery modular multiplication module combined with prime number multiplication module and -p- 1 mod 2 32 The =1 feature improves computational efficiency; the modular inverse module realizes efficient modular inverse operations based on Montgomery modular multiplication and algorithm 3; the scalar multiplication implementation module realizes a complete and efficient scalar multiplication algorithm based on Montgomery modular multiplication and modular inverse operations.

[0030] Such as figure 1 As sho...

Embodiment 2

[0036] This embodiment relates to an optimized key pair generation scheme for a digital currency hardware wallet, specifically comprising the following steps

[0037] Step 1. The user adds the seed of the key generation algorithm in the digital currency hardware wallet.

[0038] 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

The invention discloses an implementation method and system of sm2 encryption, signature and key exchange based on efficient modular multiplication. According to the Montgomery modular multiplicationmethod optimized by prime number characteristics, the multiplication operation participated by SM2 prime number is optimized, and then the modular inverse operation is carried out. Finally, the scalarmultiplication operation of signature, encryption, decryption and key exchange in SM2 is realized quickly. The invention realizes efficient modular multiplication by utilizing the characteristics ofSM2 prime numbers, and constructs efficient scalar multiplication realization and modular inverse realization based on the modular multiplication, which is suitable for the concrete 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...

Claims

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Application Information

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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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