43.3.7.5 Projective to Affine Coordinates Conversion

This service is used to perform a point coordinates conversion from a projective representation to an affine.

The operation performed is:

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

• A the input point is filled in projective coordinates (X,Y,Z) or affine coordinates for X and Y, and setting Z to 1 (pointed by {nu1PointABase,3*u2ModLength + 12}). The Point A can be the point at infinity. In this case, the u2Status returned is PUKCL_POINT_AT_INFINITY.
• Cns the 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 + 48}

The result is the point A with its (X,Y) coordinates converted to affine, and the Z coordinate set to 1.

The service name for this operation is GF2NEcConvProjToAffine.

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;

PUKCL _GF2NEcConvProjToAffine(nu1ModBase) = <Base of the ram location of P>; 
PUKCL _GF2NEcConvProjToAffine(u2ModLength) = <Byte length of P>;
PUKCL _GF2NEcConvProjToAffine(nu1CnsBase) = <Base of the ram location of Cns>; 
PUKCL _GF2NEcConvProjToAffine(nu1PointABase) = <Base of the ram location of the A point>; 
PUKCL _GF2NEcConvProjToAffine(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(GF2NEcConvProjToAffine,&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 the service works correctly:

• nu1ModBase, nu1CnsBase, nu1PointABase, nu1Workspace are not aligned on 32-bit boundaries
• {nu1ModBase, u2ModLength + 4}, {nu1CnsBase, u2ModLength + 8},{nu1PointABase, 3*u2ModLength + 12}, {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} and {nu1Workspace, 4*u2ModLength + 48}