Chapter 7. Public Key Execution Unit
7-9
PRELIMINARY—SUBJECT TO CHANGE WITHOUT NOTICE
ECC Routines
Figure 7-4. ECC F
p
Point Multiply Register Usage
It is important to note that unlike the RSA exponentiation routine, the point to be multiplied
is not expected to be in the Montgomery residue system when loaded into the PKEU. All
of the other ECC parameters are also expected to be loaded in standard format. This
includes the a and b parameters of the ECC system. In addition, the “R
2
mod N” term is
also required. This term is used by the PKEU to put the operands in the Montgomery
residue system. See the full description of this function/value below.
It is the responsibility of the host processor to provide multiplier data to the PKEU during
the operation. That is, the ‘k’ from the point multiplication ‘kP’ must be provided
dynamically by the host micro-processor in 32-bit words. Note that the host must supply
the k data starting with the most significant 32-bit word and working down to the least
significant word. Each individual word, however, is formatted msb to lsb (i.e.
“k_word[msb:lsb]”).
Post-conditions
B1 = X
2
/ X’
2
B2 = Y
2
/ Y’
2
B3 = Z
2
/ Z’
2
A2 = undefined (when XYZ = 1) or Z
2
2
(when XYZ = 0)
A3 = undefined (when XYZ = 1) or Z
2
3
(when XYZ = 0)
Unless explicitly noted, all other registers are not guaranteed to be any particular value.
Special
conditions
—
Table 7-5. ECC F
p
Point Multiply (Continued)
F
p
Point Multiply
N1
N2
N3
A0
A1
A2
A3
B0
B1
B2
B3
Initial Condition
Final Condition
XYZ
F2M
? (or Z
2
3
)
? (or Z
2
2
)
same
?
?
?
N0
?
b
prime p
prime p
y
1
(or Y
1
)
x
1
(or X
1
)
a
?
?
X
2
(or X’
2
)
Y
2
(or Y’
2
)
Z
2
(or Z’
2
)
R
2
mod N
?
k (run-time)
1 (or Z
1
)
EXP(k)
Modsize
EXP(k)_SIZE
select ‘1’ or ‘0’
‘0’ - F
p
enabled
same
set
set
same
same
ECC
same
‘1’ - ECC enabled
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Freescale Semiconductor, Inc.
For More Information On This Product,
Go to: www.freescale.com
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