ECDSA

Library for handling Elliptic Curve Digital Signature Algorithm (ECDSA) operations on a compatible curve

Functions

zz2Aff

Convert from XYZZ coordinates to affine coordinates Learn more about the XYZZ representation here: https://hyperelliptic.org/EFD/g1p/auto-shortw-xyzz-3.html#addition-add-2008-s*

function zz2Aff(uint256 x, uint256 y, uint256 zz, uint256 zzz) internal returns (uint256 x1, uint256 y1);

Parameters

Name	Type	Description
`x`	`uint256`	The X-coordinate of the point in XYZZ representation
`y`	`uint256`	The Y-coordinate of the point in XYZZ representation
`zz`	`uint256`	The ZZ value of the point in XYZZ representation
`zzz`	`uint256`	The ZZZ value of the point in XYZZ representation

Returns

Name	Type	Description
`x1`	`uint256`	The X-coordinate of the point in affine representation
`y1`	`uint256`	The Y-coordinate of the point in affine representation

zzAddN

Adds a point in XYZZ coordinates to a point in affine coordinates

function zzAddN(
    uint256 x1,
    uint256 y1,
    uint256 zz1,
    uint256 zzz1,
    uint256 x2,
    uint256 y2
)
    internal
    pure
    returns (uint256 P0, uint256 P1, uint256 P2, uint256 P3);

Parameters

Name	Type	Description
`x1`	`uint256`	The X-coordinate of the first point
`y1`	`uint256`	The Y-coordinate of the first point
`zz1`	`uint256`	The ZZ value of the first point
`zzz1`	`uint256`	The ZZZ value of the first point
`x2`	`uint256`	The X-coordinate of the second point
`y2`	`uint256`	The Y-coordinate of the second point

Returns

Name	Type	Description
`P0`	`uint256`	The X-coordinate of the resulting point
`P1`	`uint256`	The Y-coordinate of the resulting point
`P2`	`uint256`	The ZZ value of the resulting point
`P3`	`uint256`	The ZZZ value of the resulting point

zzDouble

Performs point doubling operation in XYZZ coordinates on an elliptic curve

This implements the "dbl-2008-s-1" doubling formulas from Sutherland's 2008 paper

function zzDouble(
    uint256 x,
    uint256 y,
    uint256 zz,
    uint256 zzz
)
    internal
    pure
    returns (uint256 P0, uint256 P1, uint256 P2, uint256 P3);

Parameters

Name	Type	Description
`x`	`uint256`	The X-coordinate of the point
`y`	`uint256`	The Y-coordinate of the point
`zz`	`uint256`	The ZZ value of the point
`zzz`	`uint256`	The ZZZ value of the point

Returns

Name	Type	Description
`P0`	`uint256`	The X-coordinate of the resulting point after doubling
`P1`	`uint256`	The Y-coordinate of the resulting point after doubling
`P2`	`uint256`	The ZZ value of the resulting point after doubling
`P3`	`uint256`	The ZZZ value of the resulting point after doubling

affIsOnCurve

Check if a point in affine coordinates is on the curve

function affIsOnCurve(uint256 x, uint256 y) internal pure returns (bool);

Parameters

Name	Type	Description
`x`	`uint256`	The X-coordinate of the point
`y`	`uint256`	The Y-coordinate of the point

Returns

Name	Type	Description
`<none>`	`bool`	bool True if the point is on the curve, false otherwise

affAdd

Add two points on the elliptic curve in affine coordinates

function affAdd(uint256 x0, uint256 y0, uint256 x1, uint256 y1) internal returns (uint256 x2, uint256 y2);

Parameters

Name	Type	Description
`x0`	`uint256`	The X-coordinate of the first point
`y0`	`uint256`	The Y-coordinate of the first point
`x1`	`uint256`	The X-coordinate of the second point
`y1`	`uint256`	The Y-coordinate of the second point

Returns

Name	Type	Description
`x2`	`uint256`	The X-coordinate of the resulting point
`y2`	`uint256`	The Y-coordinate of the resulting point