37.3.6.10 Point is on Elliptic Curve

This service is used to test whether or not the point is on the curve.

The operation performed is:

Status = IsPointOnCurve(X, Y, Z)

In this computation, the following parameters need to be provided:

• The input point is filled in projective coordinates (X,Y,Z) (pointed by {nu1PointBase,3*u2ModLength + 4}). This Point can be the point at infinity.
• AParam and BParam are the Elliptic Curve Equation parameters. (pointed by{nu1AParam, u2ModLength+4} and {nu1BParam, u2ModLength+4}).
• Cns the Fast Modular Constant filled (pointed by{nu1CnsBase,u2ModLength+8}).
• P the modulus filled (pointed by {nu1ModBase,u2ModLength +4}).
• The workspace not initialized (pointed by {nu1WorkSpace, 4*u2ModLength +28}.

The result is the status of the point (X,Y,Z) regarding the Elliptic Curve Equation.

The service name for this operation is ZpEcPointIsOnCurve.

PUKCL_PARAM PUKCLParam;
PPUKCL_PARAM pvPUKCLParam = &PUKCLParam;


PUKCL (u2Option) = 0;

PUKCL _ZpEcPointIsOnCurve(nu1ModBase) = <Base of the ram location of P>; 
PUKCL _ZpEcPointIsOnCurve(u2ModLength) = <Byte length of P>;
PUKCL _ZpEcPointIsOnCurve(nu1CnsBase) = <Base of the ram location of Cns>; 
PUKCL _ZpEcPointIsOnCurve(nu1AParam) = <Base of the ram location of the parameter a>; 
PUKCL _ZpEcPointIsOnCurve(nu1BParam) = <Base of the ram location of the parameter b>;
PUKCL _ZpEcPointIsOnCurve(nu1PointBase) = <Base of the ram location of the point>; 
PUKCL _ZpEcPointIsOnCurve(nu1Workspace) = <Base of the ram location of the workspace>;
...

// vPUKCL_Process() is a macro command, which populates the service name
// and then calls the library...
vPUKCL_Process(ZpEcPointIsOnCurve,&PUKCLParam); 
if (PUKCL (u2Status) == PUKCL_OK)
            {
            ...
            }
else // Manage the error

No overlapping between either input and output are allowed. The following conditions must be avoided to ensure that the service works correctly:

• nu1ModBase, nu1CnsBase, nu1PointABase, nu1AParam, nu1BParam, nu1Workspace are not aligned on 32-bit boundaries
• {nu1ModBase, u2ModLength+4}, {nu1CnsBase, u2ModLength+8}, {nu1PointABase, 3*u2ModLength +12}, {nu1AParam, u2ModLength + 4}, {nu1BParam, u2ModLength + 4}, {nu1Workspace, <WorkspaceLength>} are not in Crypto RAM.
• u2ModLength is either: < 12, > 0xffc or not a 32-bit length.
• All overlapping between {nu1ModBase, u2ModLength+4}, {nu1CnsBase,u2ModLength+8}, {nu1PointABase, 3*u2ModLength+12}, {nu1AParam, u2ModLength+4}, {nu1AParam, u2ModLength + 4} and {nu1Workspace, 4*u2ModLength+28}.