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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
In a public key system using RSA you intercept the ciphertext C=4 sent to a user whose public key is e = 7, n = 33. What is the plaintext M?
M = ________________
Fermat's Theorem:  a p-1 = 1 mod p
Euler's Theorem:Â Â a = 1 mod n
Modular arithmetic: (a*b) mod n = (a mod n * b mod n) mod n
                               (a+b) mod n = (a mod n + b mod n) mod n
RSA Algorithm (public key cryptography)
select prime numbers p,q
calculate n = p*q
calculate ?(n) = (p-1)(q-1)
select integer e relatively prime to ?(n)
find integer d which has the property e*d mod ?(n) = 1
create public key = KUÂ = [e,n]
create private key = KRÂ = [d,n]
ciphertext C = Pe mod n  Â
plaintext  P = Cd mod n Â
500
Hel-----------lo -----------Sir-----------/Ma-----------dam----------- Â----------- -----------Tha-----------nk -----------You----------- fo-----------r u-----------sin-----------g o-----------ur -----------web-----------sit-----------e a-----------nd -----------acq-----------uis-----------iti-----------on -----------of -----------my -----------sol-----------uti-----------on.-----------Ple-----------ase----------- pi-----------ng -----------me -----------on -----------cha-----------t I----------- am----------- on-----------lin-----------e o-----------r i-----------nbo-----------x m-----------e a----------- me-----------ssa-----------ge -----------I w-----------ill----------- be----------- ca-----------tch-----------