Elliptic Curve SWU Encoding Correction for Coordinate Interoperability

The patent introduces an intermediary correction mechanism using the Legendre symbol to mediate between different coordinate system implementations. The Legendre symbol acts as a mediator that detects and corrects the sign discrepancy between affine and Jacobian coordinate representations, allowing devices using different coordinate systems to interoperably generate the same cryptographic points without sacrificing computational efficiency

The patent applies parameter changes by modifying the SWU encoding function to include a sign correction parameter based on the Legendre symbol. This parameter dynamically adjusts the y-coordinate sign depending on the coordinate system being used, ensuring that the final encoded point is consistent across different implementations while maintaining the computational advantages of each coordinate system

The patent applies partial action by implementing correction only where necessary - specifically when transitioning between different coordinate systems. The Legendre symbol calculation and conditional sign adjustment are applied selectively rather than universally, adding minimal computational overhead only when interoperability between different coordinate system implementations is required

The patent uses the Legendre symbol as a lightweight, computationally inexpensive correction mechanism. The Legendre symbol calculation is a simple modular operation that can be performed efficiently, providing a cheap and effective way to correct sign discrepancies without requiring complex additional computational resources or long-term state management