Modular Inversion Script for Blockchain Elliptic Curve Arithmetic
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Solution Overview
Problem
Current blockchain systems lack the capability to perform elliptic curve arithmetic, specifically computing the modular inverse of an integer, which is essential for various cryptographic applications, within the script engine, limiting the immutability and efficiency of transactions.
Innovation Solution
A computer-implemented method is introduced that generates a modular inversion script as part of a blockchain transaction, using the extended Euclidean algorithm to compute the modular inverse, enabling its execution within the script engine for elliptic curve operations such as point addition and scalar multiplication.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If elliptic curve arithmetic is performed outside the script engine, then computational flexibility is maintained, but transaction immutability and efficiency are reduced
Solution Approach 1:
The patent pre-encodes the extended Euclidean algorithm as a modular inversion script within the blockchain transaction. This preliminary action enables the script engine to autonomously perform modular inverse computations required for elliptic curve arithmetic, eliminating the need for external computational resources and ensuring transaction immutability while maintaining computational efficiency
2Productivity
If modular inverse computation is performed externally, then computational accuracy is maintained, but user computational burden increases
Solution Approach 1:
The patent implements self-service by embedding the modular inversion functionality directly within the blockchain script engine. The modular inversion script automatically computes the required modular inverse values during transaction validation, eliminating the need for users to perform separate computational operations and reducing their computational burden while maintaining accuracy
3Reliability
If elliptic curve arithmetic is enabled in the script engine, then transaction security is enhanced, but script complexity increases
Solution Approach 1:
The patent segments the complex elliptic curve arithmetic operations into distinct, modular script components. The modular inversion script is separated as an independent functional unit that can be reused across different elliptic curve operations (point addition, scalar multiplication), reducing overall script complexity while enhancing security through standardized, verified computational routines
Data Source
AI summary
A computer-implemented method for enabling elliptic curve arithmetic to be performed using blockchain transactions, wherein the method is performed by a script generator. A first script of a first blockchain transaction is generated, wherein the first script comprises a modular inversion script configured to obtain a target integer and a modulus value and output a modular inverse of the target integer. The target integer and the modulus value are co-prime. The modular inverse is generated by iteratively computing a first sequence of the extended Euclidean algorithm with the target integer and modulus value as inputs, and using the first sequence to compute a Bezout co-efficient of the target integer, wherein the Bezout co-efficient of the target integer is output as the modular inverse. The first script is outputted for inclusion in the first blockchain transaction.