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

**Contents** • Cryptography • Encryption/Decryption Methods • Encryption/Decryption Protocols

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

**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

**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)

**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 =

**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

**Encryption/Decryption Protocols** c f CK M, K CK a d j start M g k m CK CM, K H M b n e h l n H S S H No|Yes 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. • Alice generates a random key K for DES encryption. • Alice hashes M to create H. • Alice encrypts the key K with Bob’s public key to create CK

**Encryption/Decryption Protocols** c f CK M, K CK a d j start M g k m CK CM, K H M b n e h l n H S S H No|Yes 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.

**Encryption/Decryption Protocol** c f CK M, K CK a d j start M g k m CK CM, K H M b n e h l n H S S H No|Yes 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.

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

**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

**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

**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

**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.

**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

**References** • Bruce Schneier, APPLIED CRYPTOGRAPHY: Protocols, Algorithms, and Source Code in C (2nd 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)

**Thank you for your attention.**