7-20
MPC180E Security Processor User’s Manual
PRELIMINARY—SUBJECT TO CHANGE WITHOUT NOTICE
ECC Routines
Figure 7-12. ECC F
2
m Point Add Register Usage
Table 7-13. ECC F
2
m Point Add
F
2
m Point Add
Computation
R = P + Q, where R
≡
(X
3
,Y
3
,Z
3
), P
≡
(X
1
,Y
1
, Z
1
), and Q
≡
(X
2
,Y
2
, Z
2
)
Entry name
F
2
maddPtoQ
Entry address
0x005(F
2
maddPtoQ)
Pre-conditions
A0 = X’
1
(projective coordinate in Montgomery residue system)
A1 = Y’
1
(projective coordinate in Montgomery residue system)
A2 = Z’
1
(projective coordinate in Montgomery residue system)
A3 = a’ (elliptic curve parameter in Montgomery residue system)
B0 = c’ (elliptic curve parameter in Montgomery residue system)
B1 = X’
2
(projective coordinate in Montgomery residue system)
B2 = Y’
2
(projective coordinate in Montgomery residue system)
B3 = Z’
2
(projective coordinate in Montgomery residue system)
N0 = irreducible polynomial of the ECC system
Post-conditions
A0 = X’
1
A1 = Y’
1
A2 = Z’
1
A3 = a’
B0 = c’
B1 = X’
3
B2 = Y’
3
B3 = Z’
3
Unless explicitly noted, all other registers are not guaranteed to be any particular value.
Special
conditions
The c elliptic curve parameter is a function of the ‘b’ parameter and field size:
.
All variables followed with the tick mark (‘) indicate it is in the Montgomery residue system.
c
b
2
m
2
–
=
N1
N2
N3
A0
A1
A2
A3
B0
B1
B2
B3
Initial Condition
Final Condition
a’
Z’
1
?
?
?
N0
c’
c’
irred. poly.
irred. poly.
Y’
1
X’
1
a’
X’
1
Y’
1
X’
3
Y’
3
Z’
3
X’
2
Z’
1
Y’
2
Z’
2
XYZ
F2M
EXP(k)
‘1’ - F
2
m enabled
same
Modsize
EXP(k)_SIZE
set
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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Freescale Semiconductor, Inc.
For More Information On This Product,
Go to: www.freescale.com
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..