ECC Point Doubling Hardware Architecture Using Jacobian Coordinates
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Solution Overview
Problem
Existing cryptographic technologies, particularly Elliptic Curve Cryptography (ECC), face computational intensity and high power consumption issues, making them unsuitable for widespread use in mobile and cloud computing due to the need for rapid and low-power operations.
Innovation Solution
An optimized hardware architecture that reduces storage requirements and accelerates the execution of the ECC Point Doubling (PDBL) algorithm by using only two temporary storage registers and a simple arithmetic unit for modular operations, specifically designed to perform modular addition, subtraction, multiplication, and division by 2, thereby minimizing computational steps and resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional ECC PDBL algorithm is implemented with standard temporary register requirements, then the algorithm can be executed, but storage requirements increase and execution speed decreases
Solution Approach 1:
The patent merges the functionality of three temporary registers (T1, T2, T3) into two registers by carefully orchestrating the sequence of operations. Register T1 is used for intermediate calculations, register T2 stores the squared Z coordinate, and register T3 is reused by overwriting its value with computations that depend on previously stored values, thereby eliminating the need for a third dedicated temporary register while maintaining algorithm correctness
Solution Approach 2:
The patent applies dynamic resource allocation by flexibly reusing register T3 throughout the algorithm execution. Instead of allocating fixed static registers, the implementation dynamically assigns T3 to different computational roles at different stages: first for computing 2Y1*Z1, then for storing intermediate results in the formula (Y3*X1 - X3)*T2, and finally for holding Y3*Y3/2 before the final subtraction. This dynamic reuse reduces the total register count while preserving all necessary computational states
2Reliability
If cryptographic operations are performed with high computational intensity, then security is maintained, but power consumption increases making them unsuitable for mobile devices
Solution Approach 1:
The patent changes the computational parameters by optimizing the arithmetic operations in the PDBL algorithm. By restructuring the calculation sequence and reducing the number of temporary storage operations, the implementation minimizes the total number of computational steps required. This parameter optimization reduces the energy consumption per cryptographic operation while maintaining the same security level, making ECC more suitable for mobile and resource-constrained devices
Data Source
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AI summary
An optimized hardware architecture and method introducing a simple arithmetic processor that allows efficient implementation of an Elliptical Curve Cryptography point doubling algorithm for Jacobian coordinates. The optimized architecture additionally reduces the required storage for intermediate values.