1. Key Exchange Methods Diffie-Hellman and RSA CPE 701 Research Case Study Derek Eiler | April 2012

2. Overview Today’s discussion Background: “key” cryptography concepts Diffie-Hellman key exchange Public key infrastructure (PKI) RSA key pair generation

3. Background A few “key” concepts Encryption: plaintext -> ciphertext Decryption: ciphertext -> plaintext Cryptographic function: mathematical function or algorithm used to encrypt/decrypt Key: parameter for a cryptographic function Symmetric vs. asymmetric keys

4. So four people walk into a bar… Alice, Bob, Eve, and Mallory Alice and Bob want to speak privately over a public channel Eve is always eavesdropping on Alice and Bob Mallory has malicious plans to interfere with Alice and Bob’s private conversation

5. Diffie-Hellman key exchange The concept

6. Diffie-Hellman key exchange The math: discrete logarithm problem

7. Diffie-Hellman key exchange The math: discrete logarithm in action

8. Diffie-Hellman key exchange Example using small numbers

9. RSA key generation The concept Alice generates a pair of keys, publishing one and keeping the other private Anyone may use the published key to encrypt messages intended for Alice Only Alice can decrypt messages encrypted with the public key (unless the private key was compromised somehow) Alice may also use the key pair to prove her identity

10. RSA key generation The math: factoring problem Computing the product of two prime numbers is easy (23*17 = 391) Factoring the product of two large prime numbers is “hard” Try factoring 123,018,668,453,011,775,513,049,495,838,496,2 72,077,285,356,959,533,479,219,732,245,215,17 2,640,050,726,365,751,874,520,219,978,646,938,995,647,494,277,406,384,592,519,255,732,630, 345,373,154,826,850,791,702,612,214,291,346,1 67,042,921,431,160,222,124,047,927,473,779,40 8,066,535,141,959,745,986,902,143,413

11. RSA key generation The math: public and private key pair

12. RSA key generation The math: “exponential” difficulty *Euclid’s or Stein’s algorithm are typically used to compute the GCD.

13. References Some light reading on the web RSA Laboratories: 3.6.1 What is Diffie-Hellman?3.6.1 What is Diffie-Hellman? David A. Carts: A Review of the Diffie-Hellman Algorithm and its Use in Secure Internet Protocols.A Review of the Diffie-Hellman Algorithm and its Use in Secure Internet Protocols RSA Laboratories: What is the RSA Cryptosystem?What is the RSA Cryptosystem? RSA Laboratories: RSA Factoring Challenge.RSA Factoring Challenge BigPrimes.net: Prime Numbers Archive.Prime Numbers Archive