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ECC Routines
7.3.13 ECC F
2
((A × B × R
-2
The (A × B × R
) mod N calculation is similar to the standard 'R
multiplication except an additional R is divided out. This function is ideal for those ECC
applications which work in affine coordinates. In that case, the host may use this function
to exit projective coordinates. For example, the host could find x, for x = X/Z
2
-1
(Z
)
are in the Montgomery residue system. Loading X and (Z
operand registers and initiating this function would yield x which is no longer in the
Montgomery residue system. This function operates with a minimum of 5 digits
(Modsize = 4). The complete set of I/O conditions is shown below:
Table 7-17. F
Computation
C = A * B * R
where D is the number of digits of the irreducible polynomial
Entry name
modularmultiply2 (same as F
Entry address
0x00b (modularmultiply2)
Pre-conditions
A0-3 = A (binary polynomial, exact A-location pre-selected in Control Register)
B0-3 = B (binary polynomial, exact B-location pre-selected in Control Register)
N0-3 = irreducible polynomial of the ECC system
Post-conditions
A0-3 = A operand is preserved
B0-3 = results of modular multiplication stored where the B operand was located
Unless explicitly noted, all other registers are not guaranteed to be any particular value.
Special
—
conditions
Initial Condition
irred. poly. (if N0 selected)
Figure 7-16. F
m Modular Multiplication (with double reduction) Register Usage
2
7-24
PRELIMINARY—SUBJECT TO CHANGE WITHOUT NOTICE
m Montgomery Modular Multiplication
-2
) mod N)
m Modular Multiplication (with double reduction)
2
F
m Modular Multiply (with double reduction)
2
-2
mod N, where A, B, and C are binary polynomials with order than N and R
)
p
B3
B2
B1
B0
B (if B0 selected)
A3
A2
A1
A (if A0 selected)
A0
N3
N2
N1
N0
'1' - ECC enabled
ECC
EXP(k)
XYZ
F2M
'1' - F
m enabled
2
regAsel
set (00, 01, 10, 11)
regBsel
set (00, 01, 10, 11)
regNsel
set (00, 01, 10, 11)
Modsize
set
EXP(k)_SIZE
MPC180E Security Processor User's Manual
2
-1
)
into the appropriate
Final Condition
?
?
?
C (if B0 selected)
A (if A0 selected)
?
?
?
irred. poly. (if N0 selected)
same
same
same
same
same
same
-1
' Montgomery
2
, where X and
16D
= 2
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