MATH 470 Exam 2 All Answers Correct
The 5 cryptographic algorithms - RSA public key cryptosystem - ElGamal public key cryptosystem - RSA digital signatures - ElGamal digital signatures - Diffine-Hellman key exchange
The 3 primality testing algorithms - Fermat primality test - Soloway-Strassen p...
The 5 cryptographic algorithms ✅- RSA public key cryptosystem
- ElGamal public key cryptosystem
- RSA digital signatures
- ElGamal digital signatures
- Diffine-Hellman key exchange
The 3 primality testing algorithms ✅- Fermat primality test
- Soloway-Strassen primality test
- Miller-Rabin primality test
The 2 factorization algorithms ✅- Fermat factorization method
- Quadratic sieve
The 4 discrete logarithm algorithms ✅- Definitions
- Pohlig-Hellman algorithm
- Baby step-giant step algorithm
- Index calculus
RSA public key cryptosystem ✅1. Bob chooses secret primes p and q to compute n = pq
2. Bob chooses e with gcd(e, (p-1)(q-1)) = 1
3. Bob computes d with de≡1 (mod (p-1)(q-1))
4. Bob makes n and e public, keeping p, q, and d a secret
5. Alice can encrypt message m with c≡m^e (mod n)
6. Bob can decrypt message m with m≡c^d (mod n)
, ElGamal public key cryptosystem ✅1. Bob chooses a large prime p and a primative root α
2. Bob chooses a secret integer 'a' and computes β≡α^a (mod p)
3. Bob makes (p, α, β) public
4. Alice picks a secret random integer k and computes r≡α^k (mod p)
5. Alice encrypts using t≡(β^k)(m) (mod p)
6. Alice sends the pair (r, t) to Bob
7. Bob decrypts using (t)(r^-a)≡m (mod p)
RSA digital signature ✅Alice creates her signature by...
1. Taking two large primes p and q and creating n=pq
2. Choosing Ea such that 1 < Ea < θ(n) with gcd(Ea, θ(n)) = 1
3. Calculating Da such that EaDa≡1 (mod θ(n))
4. Alice publishes (Ea, n) and keeps Da, p, and q secret
4. Signature is y≡m^Da (mod n)
5. (m, y) is made public
Bob can verify Alice's signature by...
1. Downloading (Ea, n)
2. Calculating z≡y^Ea (mod n). If z=m, the signature is valid
ElGamal digital signature ✅For Alice to sign a message m, she must...
1. Select a secret random k so that gcd(k, p-1)=1
2. Compute r≡α^k (mod p)
3. Compute s≡k^-1(m-ar) (mod (p-1))
4. Signed message is the triple (m, r, s)
Bob can verify the signature by...
1. Downloading Alice's public key (p, α, β)
2. Computing v₁≡(β^r)(r^s) (mod p)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller CertifiedGrades. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $10.79. You're not tied to anything after your purchase.
