1. Title: Cryptography Instructor: Dr. Yanqing Zhang Presented by: Jiangling, Yin Department of Computer Science Georgia State University CSC 8320 Advanced Operating Systems

2. Outline Introduction & Motivation  What is cryptography and why it is necessary? Modern cryptography 1. Private Key Cryptosystem 2. Public Key Cryptosystem 3. Comparison of Cryptographic Systems Future work

3. A Simple Example Suppose two lovers try to meet at a certain place. And the girl sends the information to the boy: meet me at ###

4. A Simple Example Instead of sending the intelligible message to the boy, the girl plays a trick and change the information. phhw ph dw fv ghvduwphqw meet me at ###

5. A Simple Example The boy receives the girl’s message and thinking…. phhw ph dw fv ghvduwphqw

6. A Simple Example If the boy happens to know Cryptography, and he may do following things… phhw ph dw fv ghvduwphqw meet me at CS department

7. A Simple Example Finally…. Meet at CS department VWXSLW What is VWXSLW ?

8. So, What Is Cryptography To make thing hard to understand if you don’t know the behind principles… To convert intelligible information into unintelligible. To hidden information.

9. 9 Application Model of Cryptography B and A (lovers!) want to communicate “securely” C (intruder) may intercept, delete, add messages secure sender secure receiver channel data, control messages data A B C

10. 10 Who Might B, A be? Distributing OS authenticated principals Web browser/server for electronic transactions (e.g., on-line purchases) on-line banking client/server DNS servers routers exchanging routing table updates

11. 11 The Language of Cryptography m plaintext message K A (m) ciphertext, encrypted with key K A m = K B (K A (m)) plaintext ciphertext K A encryption algorithm decryption algorithm A’s encryption key B’s decryption key K B

12. 12 Mapping Language Into The Example Encryption (decryption) algorithm : substitute one letter for another Plaintext: meet me at CS department Ciphertext: phhw ph dw fv ghvduwphqw Key: the mapping from the set of 26 letters to the set of 26 letters

13. Private & Public Key Cryptosystems Symmetric key cryptography: && are identical. The keys must be kept secret. The encryption and decryption functions used can be the same or different. Public key cryptography: && are different (one public, the other private). plaintext ciphertext K A encryption algorithm decryption algorithm A’s encryption key B’s decryption key K B A KK B A KK B

14. Symmetric Key Cryptography: Examples Examples: ROT13: Very simple rotation algorithm Caesar cipher: Another (better) rotation algorithm crypt: Original Unix encryption program DES: Data Encryption Standard [NIST 1993] AES: Advanced Encryption Standard Skipjack: U.S. National Security Agency developed algorithm (classified) DES: Data Encryption Standard In 1997 DES was cracked in only 140 days by a team In 1999 DES was cracked in little over 22 hours by a network of volunteers and special purpose computer.

15. Symmetric Key Cryptography: Key Issues How do sender and receiver agree on key value? How is the agreed upon key distributed to both sender and receiver in a secure fashion? plaintext ciphertext K A-B encryption algorithm decryption algorithm K A-B plaintext message, m K (m) A-B K (m) A-B m = K ( ) A-B

16. Public Key Encryption Diffie-Hellman 1976: the first public key approach proposed. Sender and receiver do not share secret key Public key is available to every one Private key is known by only receiver

17. 17 Public key cryptography plaintext message, m ciphertext encryption algorithm decryption algorithm B’s public key plaintext message K (m) B + K B + B’s private key K B - m = K ( K (m) ) B + B -

18. 18 Public key encryption algorithms need K ( ) and K ( ) such that B B.. given public key K, it should be impossible to compute private key K B B Requirements: 1 2 RSA: Rivest, Shamir, Adelson algorithm + - K (K (m)) = m B B - + + -

19. 19 RSA: Creating public/private key pair 1. Choose two large prime numbers p, q. (e.g., 1024 bits each) 2. Compute n = pq, z = (p-1)(q-1) 3. Choose e (with e<n) that has no common factors with z. (e, z are “relatively prime”). 4. Choose d such that ed-1 is exactly divisible by z. (in other words: ed mod z = 1 ). 5. Public key is (n,e). Private key is (n,d). K B + K B -

20. 20 RSA: Encryption, decryption 0. Given (n,e) and (n,d) as computed above 1. To encrypt message m (<n), compute c = m mod n e 2. To decrypt received bit pattern, c, compute m = c mod n d m = (m mod n) e mod n d Magic happens! c

21. 21 RSA example: Bob chooses p=5, q=7. Then n=35, z=24. e=5 (so e, z relatively prime). d=29 (so ed-1 exactly divisible by z). bit pattern m m e c = m mod n e 00001100 12 24832 17 c m = c mod n d 17 481968572106750915091411825223071697 12 c d encrypt: decrypt: Encrypting 8-bit messages.

22. 22 Why does RSA work? r Must show that c d mod n = m where c = m e mod n r Fact: for any x and y: x y mod n = x (y mod z) mod n m where n= pq and z = (p-1)(q-1) r Thus, c d mod n = (m e mod n) d mod n = m ed mod n = m (ed mod z) mod n = m 1 mod n = m

23. Comparison of Cryptographic Systems With suitable keys and algorithms, both methods can be secure enough for most purposes. To use symmetric cryptography, both parties must know the secret key, which can be quite inconvenient. To use public key cryptography, one only needs to find the public key to communicate with someone else, which can be a lot more convenient. Encrypting and decrypting a lot of information with public key cryptography can be painfully slow in comparison to symmetric cryptography.

24. Ongoing / Future Work --- key security

25. Quantum Cryptography Apply the phenomena of quantum physics Relies on The Heisenberg Uncertainty principle The principle of photon polarization Mehrdad S. Sharbaf,” Quantum Cryptography: A New Generation of Information Technology Sec urity System”, 2009 IEEE[2]. Mehrdad S. Sharbaf,” Quantum Cryptography: A New Generation of Information Technology Sec urity System”, 2009 IEEE

26. Quantum Cryptography (contd.) Why Quantum Cryptography is secure? when measuring the polarization of a photon, the choice of what direction to measure affects all subsequences measurements. photons can be easily polarized (by photon polarization principle) intruder can not copy unknown qubits (no-cloning theorem). presence of the intruder can be determined Harvard, and Boston University built the DARPA quantum network, the world’s first network that delivers end-to-end network security via highspeed quantum key distribution, and tested that network against sophisticated eavesdropping attacks.

27. Cryptography Based on Watermarking International Journal of Computer Science and Security (IJCSS), Volume (1) : Issue (3), 2011 Sonal Chugh & Mr. Rajesh Malik, Quality Improvement of Grey Scale and Color Images Using Cryptography and Robust Watermarking, International Journal of Computer Science and Security (IJCSS), Volume (1) : Issue (3), 2011

28. Application in wireless environment User authentication is a crucial service in wireless sensor networks (WSNs) wireless sensor nodes are typically deployed in an unattended environment, leaving them open to possible hostile network attack. However, wireless sensor nodes are limited in computing power, data storage and communication capabilities, any user authentication protocol must be designed to operate efficiently in a resource constrained environment. Yeh, H.-L.; Chen, T.-H.; Liu, P.-C.; Kim, T.-H.; Wei, H.-W. A Secured Authentication Protocol for Wireless Sensor Networks Using Elliptic Curves Cryptography. Sensors 2011, 11, 4767-4779.

29. Cryptography toolkit http://nsfsecurity.pr.erau.edu/crypto/generichash.html http://ats.oka.nu/titaniumcore/js/crypto/Cipher.sample.htm l http://ats.oka.nu/titaniumcore/js/crypto/Cipher.sample.htm l http://www.privacycrypt.com/ https://www.dlitz.net/software/pycrypto/