Mixed Affine-Jacobian ECC Hardware Architecture for Low-Power Mobile Devices
Solution Overview
Problem
Existing cryptographic implementations, particularly those using Elliptic Curve Cryptography (ECC), face computational intensity and power consumption issues, making them unsuitable for high-speed and low-power applications like mobile devices, which hinders their adoption in cloud and ubiquitous computing.
Innovation Solution
An optimized hardware architecture and method for the Elliptic Curve Digital Signature Algorithm (ECDSA) that reduces storage requirements and speeds up operations by using mixed affine-Jacobian coordinates, requiring only two temporary storage registers and incorporating a simple arithmetic unit for modular subtraction and multiplication by 2, thereby avoiding modular inversion operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional ECC point addition algorithms are used, then computational accuracy is maintained, but computational overhead and power consumption are high
Solution Approach 1:
The patent changes the coordinate system parameters from traditional affine coordinates to mixed affine-Jacobian coordinates. This parameter change allows the point addition algorithm to avoid costly modular inversion operations while maintaining computational accuracy, thereby reducing both computational overhead and power consumption in ECC operations
Solution Approach 2:
The patent extracts and eliminates the modular inversion operation from the point addition algorithm by working in mixed affine-Jacobian coordinates. By removing this computationally intensive operation, the patent significantly reduces the computational overhead and energy consumption while maintaining the security and accuracy of ECC operations
2Productivity
If traditional point addition algorithms are used, then computational accuracy is maintained, but storage requirements are high
Solution Approach 1:
The patent changes the coordinate representation parameters to mixed affine-Jacobian coordinates, which requires fewer temporary storage registers. This parameter change reduces the storage requirements from 4 temporary registers to 2 temporary registers, improving computational efficiency while maintaining accuracy
Solution Approach 2:
The patent extracts and eliminates the need for additional temporary storage registers by reorganizing the computation in mixed affine-Jacobian coordinates. This extraction of storage requirements directly improves computational efficiency by reducing the hardware resources needed for ECC operations
3Measurement precision
If modular inversion operations are performed, then computational accuracy is maintained, but operational speed decreases
Solution Approach 1:
The patent extracts and eliminates the modular inversion operation from the point addition algorithm by working in mixed affine-Jacobian coordinates. This removal of the inversion operation directly increases operational speed while maintaining computational accuracy through the alternative coordinate system
Solution Approach 2:
The patent changes the mathematical parameters from affine coordinates (which require inversion) to mixed affine-Jacobian coordinates (which avoid inversion). This parameter change enables faster operations by eliminating the computationally expensive inversion step while preserving the accuracy of the ECC computations
Data Source
AI summary
An optimized hardware architecture and method introducing a simple arithmetic processor that allows efficient implementation of an Elliptic Curve Cryptography point addition algorithm for mixed Affine-Jacobian coordinates. The optimized architecture additionally reduces the required storage for intermediate values.