Introduction to Cryptography: Key Concepts and Techniques

1. _r{{x7@xe{s7vys7@r{txzr7cx7Cr7d~zg{r7tengc Hello World and Welcome to The simple crypt Key=23 Private-key Cryptography

2. Eve ALICE BOB

3. Eve ALICE BOB Bob’s Public Key Alice’s Public Key Alice’s Public Key Alice’s Public Key Bob’s Public Key Bob’s Public Key Bob’s Private Key Alice’s Private Key

4. Bob’s Public Key Encryption Locked for Bob

5. Locked for Bob Bob’s Private Key Decryption

6. Signing Bob’s Public Key Alice’s Private Key Alice’s Private Key Singed by Alice Singed by Alice Encryption Signed by Alice & Locked for Bob

7. Decryption Signed by Alice& Locked for Bob Alice’s Public Key Bob’s Private Key Singed by Alice Verification Yes/No! Singed by Alice

8. Message This is a big secret Message I?~jhYUWEKUia Recipient’s PUBLIC key Message I?~jhYUWEKUia Message This is a big secret Recipient’s private key The Internet

9. PGP,Version 6.5.1 Manual, NetworkAssociates, 1999.

10. PGP,Version 6.5.1 Manual, NetworkAssociates, 1999.

11. Certificate Authorities • The Certificate Authority (CA) is a trusted third party • Provides the necessary authentication and security infrastructure • The CA creates and issues certificates

12. PGP,Version 6.5.1 Manual, NetworkAssociates, 1999.

13. Sondra Schneider, IFsec, June 11, 1999.

14. Using the CA to Establish Trust The CA 3- Check Signature 1- Establish a Certificate 2- send signed request and certificate Merchant Customer 4-Merchant can trust customer and may continue with trade

15. Sondra Schneider, IFsec, June 11, 1999.

16. Sondra Schneider, IFsec, June 11, 1999.

17. Authentication Protocols • General-purpose secure messaging protocols include: • SSL • S/MIME • Secure protocols for electronic commerce include: • EDI/MIME. • SET

18. SET Byte, June 1997

19. June 1997

20. June 1997

21. The Use of Smartcards Byte, June 1997

22. Minimal Key Lengths for Symmetric Ciphers, Matt Blaze and others, 1996.

23. Avoiding bogus encryption products, Matt Curtin, 1998.

24. RSAfrom the RSA FAQ • RSA is a public-key cryptosystem • take two large primes, p and q, • find their product n = pq; (n is called the modulus) • Choose, e, less than n and relatively prime to (p-1)(q-1), and find its inverse, d, mod (p-1)(q-1), which means that: ed = 1 mod (p-1)(q-1); • e and d are called the public and private exponents, respectively. • The public key is the pair (n,e); • the private key is d. • The factors p and q must be kept secret, or destroyed.

25. Two numbers are relatively prime when they share no factors in common other than 1. In other words, if the greatest common divisor of a and n is equal to 1. This is written: • gcd(a,n) = 1

26. It is difficult (presumably) to obtain the private key d from the public key (n,e). • If one could factor n into p and q, however, then one could obtain the private key d. • Thus the entire security of RSA is predicated on the assumption that factoring is difficult.

27. RSA encryption: • suppose Alice wants to send a private message, m, to Bob. • Alice creates the ciphertext c = m^e mod n, • e and n are Bob's public key. • To decrypt, Bob computes: m = c^d mod n, • and recovers the original message m; the relationship between e and d ensures that Bob correctly recovers m. Since only Bob knows d, only Bob can decrypt.

28. public-key operations take O(k^2) steps, • private key operations take O(k^3) steps, • key generation takes O(k^4) steps • where k is the number of bits in the modulus