Cryptography Protocols

Here some basic functions in our toolbox:

Authenticated Encryption:

• k = genKey() generate a symmetric key
• c = Enc(k, m) encrypts a message m with the key k assuming c includes the ciphertext, the nonce and the MAC tag.
• m = Dec(k, c) decrypts the payload c using k to get the plaintext m back. It raises an error if the MAC tag is not valid

Authenticated Encryption:

• (sKem, pKem) = genKem() returns a pair (private and public) of EC keys for key exchange
• k=ECDH(sKem1, pKem2)=ECDH(sKem2, pKem1) generates a key k by combining two key exchange pairs

Digital Signature:

• (sSig, pSig) = genSig() returns a pair (private and public) of EC keys for signature
• s = Sig(sSig, m) generate the signature s by signing the message m with the private key sSig
• Ver(pSig, s, m) verify the signature s correspond to the message m signed with the private key corresponding to pSig.

Synchronous Protocol: TLS 1.3 and the Public Key Infrastructure

TLS 1.3 has only two rounds:

• A -> B: pKemA

• ​B -> A: pKemB, *Enc(k, CertB+ Sig(pKemA

  pKemB

  CertB))*

1. What are pKemA and pKemB? What are they used for? Are they long term of short term keys?
2. Explain what Alice must do and check after receiving
3. How does Alice’s browser trust a certificate supplied by Bob’s website? What does she need to verify that certificate? ​4. Why Mallory cannot do a replay attack on Bob’s response?
4. Explain why TLS ensures Perfect-Forward Secrecy?
5. Describe how a man-in-the-middle attack could succeed on TLS/SSL? ​7. In this version of the protocol, why does not Alice sign any message so that Bob can check her identity?

Asynchronous Protocol: GPG

GPG uses two types of EC keys:

• a signature key Sig to sign messages
• a key exchange key Kem to exchange a symmetric encryption key and encrypt message

Assume that Alice is sending a GPG message to Bob:

• Alice has the GPG public key (pSignA, pKemA) and the corresponding GPG private Key (sSignA, sKemA)
• Bob has the GPG public key (pSignB, pKemB) and the corresponding GPG private Key (sSignB, sKemB)

1. Explain how Alice can sign her message m using GPG
2. Explain how Bob can verify that the message comes from Alice?
3. Explain how Alice can encrypt her message m using GPG
4. Explain how Bob can decrypt the message from Alice
5. Explain why GPG does not protect against replay attack.
6. Explain why GPG does not ensure Perfect-Forward Secrecy.