37.3.6.5 Fast Multiplying by a Scalar Number of a Point

This service is used to multiply a point by an integral constant K on a given elliptic curve over GF(p).

These two services process the Multiplying by a scalar number:

Pt_C = K × Pt_A

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

• A the input point is filled in projective coordinates (X,Y,Z) (pointed by {nu1PointABase,3*u2ModLength + 12}). This point can be the Infinite Point.
• 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, 8*u2ModLength +44}
• The a parameter relative to the elliptic curve (pointed by {nu1ABase,u2ModLength +4})
• K the scalar number (pointed by {nu1ScalarNumber,u2ScalarLength +4})

The resulting C point is represented in projective coordinates (X,Y,Z) and is stored at the very same place than the input point A. This point can be the Infinite Point.

The service name for this operation is ZpEccMulFast. This service uses Fast mode and Fast Modular Reduction for computations.

PUKCL_PARAM PUKCLParam;
PPUKCL_PARAM pvPUKCLParam = &PUKCLParam;


PUKCL (u2Option) = 0;

PUKCL _ZpEccMul(nu1ModBase) = <Base of the ram location of P>; 
PUKCL _ZpEccMul(u2ModLength) = <Byte length of P>;
PUKCL _ZpEccMul(nu1CnsBase) = <Base of the ram location of Cns>; 
PUKCL _ZpEccMul(nu1PointABase) = <Base of the ram location of the A point>; 
PUKCL _ZpEccMul(nu1ABase) = <Base of the ram location of the parameter A of the elliptic curve>; 
PUKCL _ZpEccMul(nu1KBase) = <Base of the ram location of the scalar number>; 
PUKCL _ZpEccMul(nu1Workspace) = <Base of the ram location of the workspace>; 
PUKCL_ZpEccMul(u2KLength) = <Byte length of the Scalar Number K>;
...

// vPUKCL_Process() is a macro command, which populates the service name
// and then calls the library...
vPUKCL_Process(ZpEccMulFast,&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, nu1ABase, nu1ScalarNumber, nu1Workspace are not aligned on 32-bit boundaries
• {nu1ModBase, u2ModLength + 4}, {nu1CnsBase, u2ModLength + 8}, {nu1PointABase, 3*u2ModLength+ 12}, {nu1ABase, u2ModLength + 4}, {nu1ScalarNumber, u2ScalarLength} or {nu1Workspace, 8*u2ModLength + 44} 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}, {nu1ABase, u2ModLength + 4}, {nu1ScalarNumber, u2ScalarLength} and {nu1Workspace, 8*u2ModLength + 44}