1. Overview of Cryptography Oct. 29, 2002 Su San Im CS Dept. EWU

2. Contents Cryptography Encryption/Decryption Methods Encryption/Decryption Protocols

3. Cryptography Description: The art and science of keeping messages secure by altering or transforming them m: Plaintext Encryption c: Ciphertext Decryption Original Plaintext Key

4. Criteria of Good Cryptography Confidentiality – Can decrypt only with a secret key Authentication – Identify the person at the other end of the line Integrity – No change during transit (message authentication) & detecting the loss of integrity Nonrepudiation – Know who sent the message & Documented proof of identity of sender

5. Encryption Methods Symmetric Key: Secret Key Encryption (Same key for encryption and decryption) e.g.: DES(Data Encryption Standard), AES(Advanced Encryption Standard) Asymmetric Key: Public Key Encryption (Different keys for encryption and decryption) e.g.: RSA(Rivest Shamir Adleman)

6. RSA Named after Ronald Rivest, Adi Shamir, Leonard Adleman Public Key: n, e such that 1. n=p · q 2. e is relatively prime to (p-1) · (q-1) 3. p and q are prime numbers which remain secret Private Key: n, d and d is kept secret => 1 = (e · d) mod Encryption: c = Decryption: m =

7. Example: RSA n=3337 (p=47 and q=71, 47 ·71=3337) Choose e =79 Let m=688 be the message d=1019 (  find x 1=(79 · x) mod (46 · 70=3220) ) c=688 mod 3337 = 1570 => Encrypted message m=1570 mod 3337 = 688 => Decrypted message

8. Encryption/Decryption Protocols M M, KCK CM, K M H HNo|Yes H S S start a b c d e f g h j k l m n n In this chart, boxes contain information, and paths denote activity working with or changing the information. Initially, Alice has a message M that she wishes to send signed to Bob, via a security protocol. a.Alice generates a random key K for DES encryption. b.Alice hashes M to create H. c.Alice encrypts the key K with Bob’s public key to create CK

9. Encryption/Decryption Protocols M M, KCK CM, K M H HNo|Yes H S S start a b c d e f g h j k l m n n d. Alice encrypts M using DES with key K to create CM. e. Alice encrypts the hash H with her private key to create signature S. f. Alice sends the encrypted form CK of the key K to Bob. g. Alice sends the encrypted form CM of the message M to Bob. h. Alice sends her “signature”, the encrypted form S of the hash H, to Bob.

10. Encryption/Decryption Protocol M M, KCK CM, K M H HNo|Yes H S S start a b c d e f g h j k l m n n j. Bob uses his private key to decrypt CK to recover the key K. k. Bob uses K to decrypt CM to recover the message M. l. Bob uses Alice’s public key to decrypt her signature S to recover the hash H. m. Bob hashes M to create his own version of the hash H. n. Bob compares for equality his version of the hash H with the version decrypted from Alice’s signature.

11. Public Key Encryption/Decryption Protocols Start with a letter s Convert to a number 19 Encrypt(public key of 3) 39 Decrypt(private key of 27) 19 Convert to a letter s

12. Public Key Encryption/Decryption Protocols Encryption: n = 55, e = 3, p = 5, q = 11 Let m = 19 Decryption: 3d = 1 mod 40  1= (3d) mod 40  d = 27 m = = 584,064 mod 55 = 19

13. Digital Signature Author authentication Message authentication - Assures recipients that the message was not altered in transit (integrity) Backward of Public Key Encryption & Decryption Processes Use Private Key to encrypt Public Key to decrypt

14. Mathematical Background Information Theory: How to convey info. through number Complexity Theory: How complex it is Ex) O(n) Number Theory: Find properties, patterns, and relationships of numbers. Ex) Prime Test Probability, Statistics: How to make it secure

15. Number Theory(Why Prime?) Prime Number: 1 and itself as factors When prime numbers are large enough, they're nearly impossible to factor the prime numbers into p and q.

16. Number Theory(Theorems) Fermat’s Little Theorem if 0<m < p, p: prime Then Euler’s Theorem if n = p · q p,q : prime and if 0<m<n<p Then (so )

17. References Bruce Schneier, APPLIED CRYPTOGRAPHY: Protocols, Algorithms, and Source Code in C (2 nd Eds), John Wiley & Sons, 1996. (ISBN 0-471- 12845-7) Bruce Schneier, SECRETS AND LIES: Digital Security in a networked world, John Wiley & Sons, 2000. (ISBN 0-471-25311-1) H.M. Mel and Doris Baker, CRYPTOGRAPHY DECRYPTED, Addison-Wesley, 2001. (ISBN 0- 201-61647-5)

18. Thank you for your attention.