In a public key system using RSA you intercept the ciphertext C=4 sent to a user

ID: 641042 • Letter: I

Question

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: 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 = KU = [e,n]

create private key = KR = [d,n]

ciphertext C = Pe mod n

plaintext P = Cd mod n

500

Since p and q must both be prime and n = 33 = 1

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