Montgomery Multiplication Calculator
Calculate a * b mod N using Montgomery multiplication with detailed steps.
Calculate: a * b mod N
Montgomery Form
For modulus N, choose R = 2^k > N
Montgomery representation of a:
aBar = a * R mod N
REDC Algorithm
m = (T * N') mod R
t = (T + m * N) / R
if t >= N: return t - N
else: return t
43 × 56 mod 97
= 80
R = 2^k
2^7 = 128
Verified
Yes
Montgomery Parameters
R^(-1) mod N
72
N' = -N^(-1) mod R
95
Calculation Steps
Choose R
R = 2^7 = 128
Compute R^(-1) mod N
72
Compute N' = -N^(-1) mod R
95
Convert a to Montgomery form
aBar = 43 * 128 mod 97 = 72
Convert b to Montgomery form
bBar = 56 * 128 mod 97 = 87
Compute T = aBar * bBar
T = 6264
Compute m = T * N' mod R
m = 8
Compute t = (T + m*N) / R
t = 55
Montgomery result
55
Convert back (multiply by R^(-1))
80
Verification
Direct: 43 × 56 mod 97 = 80
Montgomery result matches!