QMCS 490 - Class Today

1. QMCS 490 - Class Today • Homework back • Take-home exam will be on Blackboard after class • Public Key Crypto – Examples • Public key applications R. Smith - University of St Thomas - Minnesota

2. Homework back • We worked on it in class last time R. Smith - University of St Thomas - Minnesota

3. Private Key Public Key Cipher Text Clear Text Decryption Procedure Clear Text Encryption Procedure Public Key Encryption • Uses a pair of keys: the Private Key and the Public Key • Usually, one key of the pair decrypts what the other key encrypts, and vice versa • “Asymmetric Encryption” R. Smith - University of St Thomas - Minnesota

4. Public Key cryptography • Diffie Hellman • ‘Distributive property’ of exponents • Modulus operation R. Smith - University of St Thomas - Minnesota

5. RSA • Weird variant • Multiply two primes • Product is part of the key • 2 other numbers form rest of the key • “Public” number (often 3 or 65537) • “Private” number (the modular inverse) • Works in both directions – encrypt and decrypt R. Smith - University of St Thomas - Minnesota

6. Applications • Sharing a key • Diffie Hellman approach • RSA approach • Digital signatures • Creating one, RSA • Checking one, RSA R. Smith - University of St Thomas - Minnesota

7. Honest Abe must possess the private key in order to produce the digital signature Honest Abe’s Private Key ‘I certify that this is really true and ‘I certify that this is really true and Signature Procedure Honest Abe Signed Document Signed: Honest Abe Digital Signature Concept Document R. Smith - University of St Thomas - Minnesota

8. Alice trusts Honest Abe Alice needs proof that Abe wrote the document Abe’s public key shows that Abe signed the document with his private key ‘I certify that this is really true and Honest Abe’s Public Key Alice Signature Procedure Valid Signature Valid Document Digital Signature Digital Signature Validation R. Smith - University of St Thomas - Minnesota

9. Private Key 4327 4445219 John J. Jones 4327 4445219 John J. Jones Public Key Decryption Procedure Encryption Procedure { } Random Number Generator Secret Key Secret Key (temporary) Clear Text Clear Text Decryption Procedure Cipher Text Encryption Procedure RSA Encrypting Secret Keys • First send the secret key, then send the data R. Smith - University of St Thomas - Minnesota

10. Signature is the hash value, encrypted with the private key Associates the document’s contents with the signer Detects changes to document ‘I certify that this is really true and ‘I certify that this is really true and Hash Signed Document Private Key Digital Signature Encryption Procedure Hash Digital Signatures R. Smith - University of St Thomas - Minnesota

11. Decrypt the hash with the public key Compare with the document’s hash Signed Document Hash Public Key Hash = Digital Signature Valid? Decryption Engine Hash Digital Signature Validation R. Smith - University of St Thomas - Minnesota

12. That’s it • Questions? Creative Commons License This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. R. Smith - University of St Thomas - Minnesota