Datasheet

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Characteristics of the Operation P or Q Max Bit
Sizes
N Max Bit
Sizes
EP or EQ Max Bit Sizes
Exponent not in Crypto RAM, 4 bits window 2688 5376 <application dependent>
43.3.5.4.10 Status Returned Values
Table 43-67. CRT Service Return Codes
Returned Status Importance Meaning
PUKCL_OK Information Service functioned correctly
43.3.6 Elliptic Curves Over GF(p) Services
This section provides a complete description of the currently available elliptic curve over Prime Fields
services. These services process integers in GF(p) only.
The offered services cover the basic operations over elliptic curves such as:
• Adding two points over a curve
• Doubling a point over a curve
• Multiplying a point by an integral constant
• Converting a point’s projective coordinates (resulting from a doubling or an addition) to the affine
coordinates, and oppositely converting a point’s affine coordinates to the projective coordinates.
• Testing the point presence on the curve.
Additionally, some higher level services covering the needs for signature generation and verification are
offered:
• Generating an ECDSA signature (compliant with FIPS186-2)
• Verifying an ECDSA signature (compliant with FIPS186-2) The supported curves use the following
curve equation:
Y
2
= X
3
+ aX + b
43.3.6.1 Coordinate Systems
43.3.6.1.1 General Considerations
In this implementation, several choices have been made related to the coordinate systems managed by
the elliptic curve primitives.
There are two systems currently managed by the library:
• Affine Coordinates System where each curve point has two coordinates (X, Y)
• Projective Coordinates System where each point is represented with three coordinates (X,Y, Z)
Converting from the affine coordinates system to a projective coordinates system is performed by
extending its representation with Z = 1:
(X, Y) ⇒ (X, Y, Z= 1)
Converting from a projective coordinate to an affine one is a service offered by the PUKCL. The formula
to perform this conversion is:
(X, Y, Z) ⇒ (X / Z
2
, Y / Z
3
)
SAM D5x/E5x Family Data Sheet
Public Key Cryptography Controller (PUKCC)
© 2019 Microchip Technology Inc.
Datasheet
DS60001507E-page 1508