CS6515 EXAM 2 TEST PREP COURSEWORK
SCRIPT STUDY SHEET 2026 GRADED A+.
โ Euler's Theorem. Answer: - for any N,z where gcd(z, N) = 1; that is
they are relatively prime:
- then z^(phi(n)) = 1 mod N
phi(N) = # of integers between 1 & N which are relatively prime to N
phi(N) - is called Euler's totient function
Note: Euler's Theorem is a generalization of Fermat's little theorem
for arbitrary N
โ RSA Protocol. Answer: 1. Bob picks 2 n-bit random primes p & q
2. Bob chooses e relatively prime to (p-1)(q-1)
3. Bob publishes his public key (p*q, e)
4. Bob computes his private key: d ::: e^-1 mod (p-1)(q-1)
1. Alice looks up Bob's public key (pq, e)
2. Alice computes y:::m^e MOD N
1. Bob receives y
2. Bob decrypted: computes y^d MOD N ::: m
