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CS 465 Introduction to Security and Privacy

Public Key Encryption

Ungraded Quiz

  • Can you draw a diagram for hybrid encryption?

  • Can you show cryptographic notation for the diagram?

Key Concepts

Public Key Cryptography

public key cryptography
  • Each party creates a separate key pair, (public key, private key).
  • If Alice knows Bob’s public key, she can encrypt a message using his public key (eB) and only Bob can decrypt the message using his private key (dB).
    • c = EeB(m)
    • m = DdB(c)
  • Bob must keep his private key secret, otherwise anybody could decrypt his messages.
  • Standard public key cryptography algorithm is called RSA — provides computational security
  • Typically use padding with RSA to turn a deterministic encryption into one that incorporates some randomness. A common standard is PKCS#1 v2.

Hybrid Encryption

  • Usually, we use public key cryptography to bootstrap a shared, symmetric key.
  • This is because encrypting and decrypting with a symmetric key is much fater than encrypting and decrypting with public key cryptography.
  • Alice can choose a symmetric key, then encrypt it with Bob’s public key and send it to him. Now they both have a symmetric key they can use to encrypt and decrypt messages to each other.
  • See Figure 2.8, page 38
  • Alice and Bob can choose a new symmetric key each time they communicate, so we call this a session key.

Digital Signatures

digital signatures

  • Alice can sign (encrypt) a message with her private key (sA). Bob can verify (decrypt) the message with Alice’s public key (vA).

    • Here we use (v, s) to represent the (public key, private key).
    • Be sure to use separate keys for encryption/decryption and signing/verifying. signing/verifying.

  • See Figure 2.9, page 40

  • Digital signatures provide:

    • data origin authentication — we can verify who signed the message
    • data integrity — we can verify whether the message is the same as what was signed
    • non repudiation — the signer can’t claim they didn’t sign the message (unless someone stole their private key)

  • Use of public key cryptography by the general public is hard because it requires you to keep your private key safe and to have a reliable way to distribute your public key to others. These are key management issues.

Exercise