43.3.7.2 Point Addition

This service is used to perform a point addition, based on a given elliptic curve over GF(2ⁿ).

Please note that this service is not intended to add the same point twice. In this particular case, use the doubling service (see Point Doubling).

The operation performed is:

Pt_C = Pt_A + Pt_B

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

• Point 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.
• Point B the input point is filled in projective coordinates (X,Y,Z) (pointed by {nu1PointBBase,3*u2ModLength + 12}). This point can be the Infinite Point.
• Cns the Fast Modular Constant filled (pointed by {nu1CnsBase,u2ModLength + 12})
• P the modulus filled (pointed by {nu1ModBase,u2ModLength + 4})
• The a parameter relative to the elliptic curve equation (pointed by {nu1ABase,u2ModLength + 4})
• The workspace not initialized (pointed by {nu1WorkSpace, 7*u2ModLength + 40}

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

PUKCL_PARAM PUKCLParam;
PPUKCL_PARAM pvPUKCLParam = &PUKCLParam;
//Depending on the function the Random Number Generator
//must be initialized and started
//following the directives given for the RNG on the chip
PUKCL(u2Option) = 0;
PUKCL_GF2NEccAdd(nu1ModBase) = <Base of the ram location of P>;
PUKCL_GF2NEccAdd(nu1CnsBase) = <Base of the ram location of Cns>;
PUKCL_GF2NEccAdd(u2ModLength) = <Byte length of P>;
PUKCL_GF2NEccAdd(nu1PointABase) = <Base of the ram location of the A point>;
PUKCL_GF2NEccAdd(nu1PointBBase) = <Base of the ram location of the B point>;
PUKCL_GF2NEccAdd(nu1ABBase) = <Base of the ram location of the a Parameter>;
PUKCL_GF2NEccAdd(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(GF2NEccAddFast, 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 the service works correctly:

• nu1ModBase,nu1CnsBase, nu1PointABase, nu1PointBBase, nu1ABBase, nu1Workspace are not aligned on 32-bit boundaries
• {nu1ModBase, u2ModLength + 4}, {nu1CnsBase, u2ModLength + 8}, {nu1PointABase, 3*u2ModLength+ 12}, {nu1PointBBase, 3*u2ModLength + 12}, {nu1ABase,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}, {nu1PointBBase, 3*u2ModLength + 12}, {nu1ABase,u2ModLength + 4} and {nu1Workspace, 5*u2ModLength + 32}