Elliptic Curve Shared Key Generation Reducing Squaring Operations
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Solution Overview
Problem
The calculation cost of key sharing processes using the McCullagh-Barreto (MB) method is high, leading to processing delays, particularly in low-performance devices within Internet of Things (IoT) systems, due to the large number of squaring and multiplication operations required in the bilinear map on elliptic curves.
Innovation Solution
A shared key generation method that calculates a first value using an algorithm on an extension field of a prime field from points on an elliptic curve, then uses this value and a private key to generate a shared key through a final exponentiation process, reducing the number of squaring and multiplication operations by preliminary calculations and efficient exponentiation techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the MB method is used for key sharing, then mutual authentication function is achieved, but calculation cost becomes large leading to processing delay
Solution Approach 1:
The patent performs preliminary calculations of the Miller algorithm before the final exponentiation step. By pre-computing intermediate values and storing them, the system reduces the computational burden during the actual key sharing process, thereby reducing processing delay while maintaining authentication functionality
Solution Approach 2:
The patent divides the key sharing process into distinct segments: the Miller algorithm execution, intermediate value storage, and final exponentiation. This segmentation allows for optimized computation at each stage and enables parallel processing where applicable, reducing overall processing time
2Reliability
If exponentiation and bilinear map are executed in the MB method, then key sharing is achieved, but the number of squaring and multiplication operations increases calculation cost
Solution Approach 1:
The patent pre-calculates and stores intermediate values from the Miller algorithm before performing the final exponentiation. This preliminary action reduces the number of operations needed during the critical key generation phase, lowering calculation cost while maintaining key sharing functionality
Solution Approach 2:
The patent combines the results of the Miller algorithm with the final exponentiation in an optimized manner. By merging these computational steps and reusing intermediate results, the system reduces the total number of squaring and multiplication operations required
Data Source
AI summary
An information processing terminal generates a shared key by a public key cryptosystem using an identifier. The information processing terminal calculates a first calculation value by using an algorithm that outputs an element on an extension field of a prime field from two points on an additive cyclic group on an elliptic curve that is defined by the prime field. The information processing terminal holds the first calculation value. The information processing terminal calculates a second calculation value from a variable using an identifier of a sharer that shares the shared key, a private key of the information processing terminal, and the algorithm. The information processing terminal generates the shared key by executing a final exponentiation to each of the exponentiation of the first calculation value and the second calculation value.