SM2 Digital Signature Generation Efficiency via Parameter Regeneration
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The SM2 digital signature generation algorithm is limited by the inefficiency of large integer multiplication and modular operations, which affects its operational efficiency, despite being applied in user identity authentication and information integrity checks.
Innovation Solution
A method and device that regenerate digital signature parameters r and s by performing specific large integer operations, such as modular inverses and additions, to reduce the number of required large integer operations, thereby improving efficiency by potentially dispensing with one large integer multiplication or modular multiplication operation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the standard SM2 digital signature generation algorithm is used, then the digital signature can be generated with complete security functions, but the operational efficiency is limited due to multiple large integer multiplication and modular operations
Solution Approach 1:
The patent changes the computational parameters by transforming the calculation of s from requiring modular multiplication to requiring only modular addition and multiplication by small integers. Specifically, it uses the transformation s = (k - r·dA) mod n → s = (k + (n-r)·dA) mod n, where (n-r) is pre-calculated, converting a complex modular multiplication into simpler operations that can be performed more efficiently.
Solution Approach 2:
The patent performs preliminary calculations of certain values before the main signature generation process. It pre-calculates (n-r) mod n and stores it for later use, so that during signature generation, only simple addition and multiplication operations are needed instead of complex modular multiplications. This preliminary preparation reduces the computational burden during actual signature generation.
2Reliability
If large integer multiplication and modular operations are performed as specified in the standard algorithm, then the digital signature parameters r and s can be correctly generated, but the computational time increases
Solution Approach 1:
The patent extracts and removes the computationally expensive modular multiplication operation from the signature generation process. By rewriting the formula and using pre-calculated values, it extracts the heavy computational part (modular multiplication) and replaces it with lighter operations (modular addition and multiplication by small integers), thereby reducing computational time while maintaining correctness.
Solution Approach 2:
The patent uses copying of pre-calculated values to avoid repeated expensive computations. It copies and stores (n-r) mod n for reuse during signature generation, eliminating the need to perform complex modular arithmetic operations repeatedly. This copying strategy maintains mathematical correctness while significantly reducing computational time.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
Disclosed are a method and device for generating a digital signature. The method comprises: a device generating a digital signature parameter r that meets an effective determining condition; generating a digital signature parameter s according to the following formula s = ((1 + dA)-1·(r + k)-r) mod n, by using a private key dA, a random number k, r, and an elliptic curve parameter n, a value range of k being [1, n-1]; determining if the generated s is 0; if s is 0, regenerating r that meets the effective determining condition, and regenerating s by using dA, the regenerated k with the value range of [1, n-1] and the regenerated r and n, until s is not 0; converting data types of r and s that is not 0 into byte strings, to obtain a digital signature (r, s). According to the technical solutions provided by embodiments of this application, a digital signature parameter s is obtained by using a simplified calculation formula, and the number of times that big integers are calculated can be reduced, so that the calculation efficiency of generating a digital signature based on an SM2 digital signature generation algorithm is improved.