ELLIPTIC CURVE ARITHMETIC IN SCRIPT

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ELLIPTIC CURVE ARITHMETIC IN SCRIPT

This abstract first appeared for US patent application 20250103299 titled 'ELLIPTIC CURVE ARITHMETIC IN SCRIPT

Original Abstract Submitted

a computer-implemented method for enabling elliptic curve arithmetic to be performed using blockchain transactions. a first script of a first blockchain transaction is generated, comprising a modular inversion script configured to obtain a target integer and a modulus value, and output a modular inverse of the target integer. the modular inverse is generated by generating a sequence of squaring values; for each set bit of a reduced modulus value expressed in binary, including the corresponding squaring value of the sequence of squaring values in a result; multiplying together the squaring values of the result to generate a resultant value; and computing a modulus of the resultant value with respect to the modulus value, wherein the modulus of the resultant value is output as the modular inverse, and outputting the first script for inclusion in the first blockchain transaction.