Public Key Cryptography



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Lecture 2 Public Key Cryptography

Public Key Cryptography

  • New paradigm introduced by Diffie and Hellman
  • The mailbox analogy:
    • Bob has a locked mailbox
    • Alice can insert a letter into the box, but can’t unlock it to take mail out
    • Bob has the key and can take mail out
  • Encrypt messages to Bob with Bob’s public key
    • Can freely distribute
  • Bob decrypts his messages with his private key

Requirements

  • How should a public key scheme work?
  • Three main conditions
    • It must be computationally easy to encrypt or decrypt a message given the appropriate key
    • It must be computationally infeasible to derive the private key from the public key
    • It must be computationally infeasible to determine the private key from chosen plaintext attack

How does PKC Work?

  • The public key is used by the sender to encrypt information, whereas the private key is used by a recipient to decrypt it. The public key can be shared without compromising the security of the private one. All asymmetric key pairs are unique, so a message encrypted with a public key can only be read by the person who has the corresponding private key.
  • The keys of a pair are mathematically related, and their length is much longer than those used in symmetric cryptography. So, it is not easy to decipher the private key from its pubic counterpart. RSA is one of the most common algorithms for asymmetric encryption in use today.

Exchanging keys

  • Alice and Bob want to communicate using a block cipher to encrypt their messages, but don’t have shared key
  • How do Alice and Bob get a shared key?

Solution 1

  • Alice sends the key along with her encrypted message
  • Eve sees encrypted message and key
  • FAIL!

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