43.3.7.8 Point is on Elliptic Curve

This service is used to test whether 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 points filled in projective coordinates (X, Y, Z) (pointed by {nu1PointBase, 3*U2ModLength + 4}). This point can be 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 + 8})
• The workspace not initialized (pointed by {nu1WorkSpace, 4*u2ModLength + 28})

The service name for this operation is GF2NEcPointIsOnCurve.

PUKCL_PARAM PUKCLParam;
PPUKCL_PARAM pvPUKCLParam = &PUKCLParam;

// ! The Random Number Generator must be initialized and started
// ! following the directives given for the RNG on the chip

PUKCL (u2Option) = 0;

// Depending on the option specified, not all fields should be filled
PUKCL _GF2NEcPointIsOnCurve(nu1ModBase) = <Base of the ram location of P>;
PUKCL _GF2NEcPointIsOnCurve(u2ModLength) = <Byte length of P>;
PUKCL _GF2NEcPointIsOnCurve(nu1CnsBase) = <Base of the ram location of Cns>;
PUKCL _GF2NEcPointIsOnCurve(nu1PointABase) = <Base of the A point>;
PUKCL _GF2NEcPointIsOnCurve(nu1AParam) = <Base of the ram location of the parameter a>;
PUKCL _GF2NEcPointIsOnCurve(nu1BParam) = <Base of the ram location of the parameter b>;
PUKCL _GF2NEcPointIsOnCurve(nu1PointBase) = <Base of the ram location of the point>;
PUKCL _GF2NEcPointIsOnCurve(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...
vPUKC L_Process(GF2NEcPointIsOnCurve,
pvPUKCLParam);
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 and 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, 4*u2ModLength + 28} 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}, {nu1BParam, u2ModLength + 4} and {nu1Workspace, 4*u2ModLength + 28}