Chapter 7. Public Key Execution Unit
7-21
PRELIMINARY—SUBJECT TO CHANGE WITHOUT NOTICE
ECC Routines
7.3.10 ECC F
2
m Point Double
This function is extensively utilized by the point multiply routine. However, its value as a
stand-alone routine to the host processor is extremely limited. As a result, the information
provided on the routine is primarily for testing and debug purposes.
Figure 7-13. ECC F
2
m Point Double Register Usage
Table 7-14. ECC F
2
m Point Double
F
2
m Point Double
Computation
R = Q + Q = 2 * Q, where R
≡
(X
3
,Y
3
,Z
3
), and Q
≡
(X
3
,Y
3
, Z
3
)
Entry name
F
2
mdoubleQ
Entry address
0x006(F
2
mdoubleQ)
Pre-conditions
B1 = X’
1
(projective coordinate in Montgomery residue system)
B2 = Y’
1
(projective coordinate in Montgomery residue system)
B3 = 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)
N0 = prime p (modulus) of the ECC system
Post-conditions
B1 = X’
3
B2 = Y’
3
B3 = Z’
3
A3 = a’
B0 = c’
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.
While not explicitly mentioned or necessary, the contents registers A0, A1, and A2 a left undisturbed
in anticipation that these will store the generator point (P) during a point multiply.
c
b
2
m
2
–
=
N1
N2
N3
A0
A1
A2
A3
B0
B1
B2
B3
Initial Condition
Final Condition
a’
same
?
?
?
N0
b’
c’
irred. poly.
irred. poly.
Y’
1
X’
1
a’
same
same
X’
3
Y’
3
Z’
3
Z’
1
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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