A low overhead method and architecture for side-channel attack resistance in elliptic curve arithmetic

A computer-implemented method for adding side-channel attack resistance in elliptic curve arithmetic comprising the steps of:

• providing a computer processing system that includes at least one elliptic curve computational unit:
• performing, within the at least one elliptic curve computational unit, an elliptic curve arithmetic operation with a sequence of field operations:
• receiving an elliptic curve numerical input that includes at least one elliptic curve coefficient of an elliptic curve and utilizing the at least one elliptic curve coefficient of the elliptic curve in the elliptic curve arithmetic operation;
• receiving an elliptic curve coefficient randomization numerical input that includes a numerical value and utilizing the numerical value of the elliptic curve coefficient randomization numerical input in the elliptic curve arithmetic operation;
• computing at least one new and substantially equivalent elliptic curve representation for the at least one elliptic curve coefficient of the elliptic curve by performing at least one field operation with the elliptic curve numerical input and the elliptic curve coefficient randomization numerical input;
• utilizing the at least one new and substantially equivalent elliptic curve representation in the sequence of field operations;
• and
• generating at least one numerical result from the elliptic curve arithmetic operation.