Datasheet

Note: Most of the Elliptic Curve computations are reduced modulo P. In many functions the
reductions are made with the Fast Reduction.
• Cns the Modular Constant (often pointed by {nu1CnsBase,u2ModLength + 12}): This parameter
contains the Modular Constant associated to the Modulus
Important: The Modular Constant must be calculated before using the GF(p) Elliptic Curves
functions by a call to the Setup for Modular Reductions with the GF(p) option (see Modular
Reduction Setup in the 43.3.5.1 Modular Reduction section).
43.3.6.2 Point Addition
43.3.6.2.1 Purpose
This service is used to perform a point addition, based on a given elliptic curve over GF(p). Please note
that:
• This service is not intended to add the same point twice. In this particular case, use the doubling
service
(see 43.3.6.4 Fast Point Doubling).
43.3.6.2.2 How to Use the Service
43.3.6.2.3 Description
The operation performed is:
Pt
C
= Pt
A
+ Pt
B
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.
• 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 +8})
• P the modulus filled (pointed by {nu1ModBase,u2ModLength +4})
• The workspace not initialized (pointed by {nu1WorkSpace, 5*u2ModLength +32}
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 ZpEccAddFast. This service uses Fast mode and Fast Modular
Reduction for computations.
Important: Before using this service, ensure that the constant Cns has been calculated with
the Setup of the Modular Reduction functions.
SAM D5x/E5x Family Data Sheet
Public Key Cryptography Controller (PUKCC)
© 2019 Microchip Technology Inc.
Datasheet
DS60001507E-page 1510