Elliptic Curve Scalar Multiplication Optimization via Dynamic Window Width
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Solution Overview
Problem
The challenge in elliptic curve cryptography is the difficulty in determining the optimum window width for Non-Adjacent Form (NAF) or Modified Non-Adjacent Form (MOF) representations, which affects the pre-computation amount and computation cost for scalar multiplication, leading to inefficient processing.
Innovation Solution
An apparatus and method that estimate the optimum pre-computation amount based on the scalar value, perform pre-computation, and generate a MOF representation to optimize the scalar multiplication computation, reducing the computation cost by minimizing the number of pre-computation executions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the window width is increased to reduce the number of additions in scalar multiplication, then the computation efficiency is improved, but the pre-computation amount exponentially increases
Solution Approach 1:
The patent applies dynamics by making the window width adjustable rather than fixed. The computation unit can dynamically change the window width during scalar multiplication operations, allowing optimization between pre-computation cost and computation efficiency based on the specific scalar value being processed. This resolves the contradiction by enabling adaptive selection of window width to balance both factors.
Solution Approach 2:
The patent changes the parameter of window width from a static value to a variable that can be adjusted. By modifying this parameter based on the scalar value characteristics, the system can optimize the balance between pre-computation amount and computation efficiency, preventing the exponential increase in pre-computation while maintaining high computation speed.
2Productivity
If the window width is determined before computation to enable pre-computation, then the computation process can be optimized, but the optimum window width cannot be determined
Solution Approach 1:
The patent applies preliminary action by performing analysis of the scalar value before the main computation to determine the appropriate window width. The computation unit examines the scalar value characteristics in advance and selects an optimal window width, enabling both optimization and ease of operation by making the determination process systematic rather than trial-and-error.
Solution Approach 2:
The system incorporates feedback by evaluating the scalar value and adjusting the window width based on this information. The computation unit uses feedback from analyzing the scalar value's properties to determine the optimal window width, making the process both optimized and operationally simple through automated decision-making.
Data Source
AI summary
An apparatus computing scalar multiplication of a point on an elliptic curve by a scalar value includes an estimation unit configured to estimate a pre-computation amount based on the scalar value, a pre-computation unit configured to perform pre-computation based on the point on the elliptic curve by using the estimated pre-computation amount, a generating unit configured to generate an internal representation of the scalar value by using the estimated pre-computation amount, and a computation unit configured to output a result of the scalar multiplication of the point based on the result of the pre-computation and the internal representation.