1. Montgomery Modular Multiplication
By K. C. Cinnati Loi
For EE 800: Circuit Elements in Digital Computations Project Proposal

2. Long Division Algorithm
(mod) ^ ^
Reference:

3. Montgomery Algorithm TR-1 mod N Function REDC(T) m ← (T mod R)N’ mod R
t ← (T + mN) / R
if t ≥ N then return t – N
else return t
R: R = 2b, R > N and gcd(R, N) = 1
0 < R-1 < N, 0 < N’ < R and RR-1 – NN’ = 1

4. Montgomery Algorithm (cont.)
xy mod N
REDC(x) = xR-1 mod N
REDC(y) = yR-1 mod N
Let z = REDC(xy) = (xy)R-1 mod N
REDC(x) * REDC(y) = (xy)R-1R-1 mod N = zR-1 mod N
REDC(x) * REDC(y) = REDC(z)

5. Project Proposal FPGA Implementation of the processor proposed in:
J. Huang, H. Li, P. Sweany, “An FPGA Implementation of Elliptic Curve Cryptography for Future Secure Web Transaction”, International Conference on Parallel and Distributed Computing Systems (PDCS 2007), pp. 296 – 301, Sept
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