1. Bronson Jastrow

2. Outline  What is cryptography?  Symmetric Key Cryptography  Public Key Cryptography  How Public Key Cryptography Works  Authenticating sources  Hybrid Cryptosystems  Perfect Forward Secrecy  Attacks on Public Key Systems

3. What is Cryptography?  The securing of communications between parties.  Many ways to implement cryptography  Four basic goals of cryptography: Confidentiality Integrity Authentication Non-repudiation

4. Goals of Cryptography  Confidentiality: Ensure only intended recipients have the means to read data.  Integrity: Ensure intended recipients have received data unaltered by a third party.

5. Goals of Cryptography  Authentication: Ensure subsequent messages from a source can be verified as originating from that source.  Non-Repudiaton: Ensure messages are traceable back to only the originator for when disputes arise.

6. Symmetric Key Cryptography  The same key is used for both encrypting and decrypting data.  Shared Secret (One key shared by all).  Known as Private Key Cryptography.  Not ideal for exchange over unsecured networks.

7. Public Key Cryptography  Different keys are used for encryption and decryption.  Encrypt with public key.  Decrypt with private key.  Known as Asymmetric Key Cryptography.

8. Public Key Cryptography  Public keys may be shared.  Private keys must be kept secret.  Public keys may be exchanged over unsecured networks.  The keys are mathematically linked.  Computationally infeasible to compute the private key from the public key.  Disadvantage: Encryption and decryption are slow.

9. Trap Door Function  A function which is easy to compute in one direction, but difficult in the opposite direction. Integer Factorization Discrete Logarithm Elliptic Curve  Used for implementation of public key cryptography.  Example: RSA is based on Integer Factorization

10. Integer Factorization  Hard to decompose an integer into its prime factorized form.  Easy to compute an integer from its prime factorized form.  Ex: What is the prime factorization of 247? 13*19

11. Integer Factorization  No efficient way to determine prime factorization.  Even more difficult to determine a semiprime (a product of two primes).

12. RSA-768 Factorization  2009 – A 768 bit (232 decimal) semiprime generated by the RSA algorithm was factored.  Estimated 1,500 years of 2.2Ghz AMD Opteron processing.  RSA-1024 is considered 1,000 harder to crack

13. RSA-768 Perspective  RSA-768 = 123018668453011775513049495838496272077285356959533479 21973224521517264005 072636575187452021997864693899564749427740638459251925 57326303453731548268 507917026122142913461670429214311602221240479274737794 08066535141959745985 6902143413  RSA-768 = 334780716989568987860441698482126908177047949837137685 68912431388982883793 878002287614711652531743087737814467999489 * 367460436667995904282446337996279526322791581643430876 42676032283815739666 511279233373417143396810270092798736308917

14. Digital Signatures  Messages may be signed with the sender’s private key.  Signatures can be verified by the matching public key.  Verification means the message is from the owner of the private key  Verification also means the message has not been tampered with.  Signer cannot deny having signed message.

15. Public Key vs. Symmetric Key Cryptography  Public Key Cryptography Keys can be exchanged safely over the internet. Slow encryption and decryption times. Signatures to verify identity.  Symmetric Key Cryptography Key exchange over internet is insecure Fast encryption and decryption compared to public key cryptography.

16. Hybrid Cryptosystems  Combining of Symmetric Key and Public Key algorithms.  Exchange public keys.  Encrypt symmetric key to use for session.  Send encrypted symmetric key.  Exchange messages using symmetric key.

17. Hybrid Cryptosystems  SSL/TLS uses hybrid cryptosystems to secure internet transactions. Ex. Email, Banking  Problem: How to protect users from man-in-the-middle attacks

18. Key Exchange  How does a user know that the party they exchange keys with is legitimate?  Answer: Certificate Authorities.  Certificate Authority is a trusted third party.  Certificate from website is sent to user.  Certificate contains public key, and a copy signed by a certificate authority.

19. Key Revocation  Key Compromise  Affiliation Change  Key Superseded

20. Key Revocation  What happens when a key is compromised?  Certificate Revocation List (CRL)  Keep a list of revoked public keys  When revoked, list a new public key

21. Key Revocation  How to handle revocation requests?  Depends on setup Owner of private key Compound Principals

22. Notifying Users  Push from server to client Susceptible to DOS attack  Download by user from centralized server.  Set a short expiration date on updated list

23. Perfect Forward Secrecy  All past communication is safe even if a private key is compromised.  Session keys must not be derived if long term keys are lost.  Problem: Private keys decrypt symmetric keys and verify identity.  Solution: Use private keys only to verify identity.

24. Diffie-Hellman Key Exchange  D-H key exchange can be used to achieve perfect forward secrecy  Allows two hosts to create symmetric keys through an insecure network.  Works between hosts which have never communicated.

25. Diffie-Hellman Key Exchange AliceBob SecretPublicCalculateSendsCalculatePublicSecret ap,gp,g ->b ap,g,Ag a mod p = AA ->p,gb ap,g,A<- Bg b mod p = Bp,g,A,Bb a, sp,g,A,BB a mod p = sA b mod p = sp,g,A,Bb, s  p is prime  g is a primitive root mod p

27. Diffie-Hellman In Practice  Typically uses elliptic curve instead of discrete logarithm  Browser support is lacking Firefox Chrome  Performance issues for TLS handshakes

28. Attacks on Public Key Systems  Easiest way is to break people, not break encryption.  Broken algorithm: Messages can be decrypted without private key.  Totally broken algorithm: Private key can be recovered from public key.  Current systems are considered secure if key length is long.

29. Public Key Cryptography Conclusion  Secures communication over unsecured networks.  Allows authentication, integrity checks, and non-repudiation.  Used in conjunction with symmetric key encryption in TLS/SSL.

30. Sources  [1] Bernat, V. (2011). SSL/TLS & Perfect Forward Secrecy. Retrieved 10 2, 2013, from Vincent Bernat Blog: http://vincent.bernat.im/en/blog/2011-ssl-perfect-forward- secrecy.html  [2] Cooper, A. D. (1998). A closer Look at Revocation and Key Compromise in Public Key Infrastructures. Gaithersburg: National Institute of Standards and Technology.  [3] Dev-NJITWILL. Crypto.  [4] Diffie, W., & Hellman, M. E. (1976). New Directions in Cryptography. IEEE.  [5] Göthberg, D. Public Key Encryption. Sweden, Sweden.  [6] Kleinjung, T. (2010). Factorization of a 768-bit RSA modulus.  [7] Menezes, A. J., van Oorschot, P. C., & Vanstone, S. A. (1996). Handbook of Applied Cryptography. CRC Press.  [8] Rescorla, E. (2006). Diffie-Hellman Key Exchange - A Non-Mathematician's Explanation. ISSA Journal, 7.  [9] Ristic, I. (2013, June 25). SSL Labs: Deploying Forward Secrecy. Retrieved 10 10, 2013, from Qualys Community: https://community.qualys.com/blogs/securitylabs/2013/06/25/ssl-labs-deploying- forward-secrecy  [10] Vinck, A. H. (2012, May 12). Introduction to Public Key Cryptography. Duisburg- Essen, Germany. Retrieved from http://www.exp-math.uni- essen.de/~vinck/crypto/script-crypto-pdf/add-to-3.pdf