1. Cryptography Lecture 1: Introduction Piotr Faliszewski

2. Introduction Instructor:  Piotr Faliszewski  Office: 70-3575  pf@cs.rit.edu Website:  http://www.cs.rit.edu/~pf/crypto

3. Prerequisites Mathematics  Some number theory We will revise what we need!  Some probability  Etc. Programming

4. Course Plan WeekMondayWednesday 1IntroductionClassic ciphers 2Introduction to number theory 3Number theoryRSA 4Primality testing and factoring 5ReviewMT-1 6Discrete logarithm, digital signatures 7Block ciphers / DES / hash functions 8Finite fieldsAES 9Security protocolsComsoc (??) 10reviewMT-2

5. Cryptography Kryptos (hidden) Graphein (writing) Graphein (writing) Steganos (covered) Steganography Two approaches to security of information  Steganography: hiding the message  Cryptography: scrambling the message Often combined Cryptology, cryptanalisis, cryptography...

6. Cryptography in a Nutshell Cryptography in the classical era  Roman ciphers Ceasar’s cipher: shift-by-three  A  D, B  E, … Greek letters cipher  Write in latin, but using greek letters  Atbash Substitution cipher for the hebrew alphabet  Kama-sutra 45 th art: the art of secret writing Security: Via concealing the algorithm

7. Cryptography in a Nutshell “Medieval” times  Substitution ciphers Frequency analysis!  Polyalphabetic ciphers Vigenére cipher “unbreakable” cipher (considered so even in early 20 th century!!!) Modern era  Kerckhoff’s principle  Breaking of the Vigenére cipher Security: Via hiding a relatively short key

8. Kerckhoff’s Principle Means to achieve security  Unknown method/small key  Unknown symmetric key  Unknown public key Kerckhoff’s principle  The algorithm is known  Security rests on the key used within the algorithm Security through hardness  Key should be long…  … but not all ciphers use their keys efficiently  Other applications… political science and voting!

9. Cryptography in a Nutshell Twentieth century  Codetalkers Using simple codes based on very rare native languages (e.g., U.S. Navy’s Navajo program)  Electromechanical devices Enigma and others  Cryptography for the masses DES, AES Public-key cryptography Security: through computational hardness

10. Ciphers symmetricpublic-key substitution DES AES RSA ElGamal shift affine Diffie-Hellman (key exchange)

11. The Basic Scenario Two parties communicate  Alice and Bob  Insecure channel: Eve is listening! Scenario:  Alice: plaintext  ciphertext (using some algorithm)  Ciphertext sent to Bob (Eve receive’s it as well)  Bob: ciphertext   plaintext

12. Information Security Information security requires  Confidentiality – messages stay secret  Data integrity – messages are not altered  Authentication – Bob knows that Alice sent the message  Non-repuditation – Alice can’t deny sending the message

13. Possible Attacks Attacks on confidentiality  Ciphertext only  Known plaintext  Chosen plaintext  Chosen ciphertext  Key-only (public-key cryptography)

14. Applications of Cryptography Cryptographic applications  Digital signatures  Identification/password protection  Key establishment  Secret sharing  Security protocols  Electronic cash  Games  Zero-knowledge techniques

15. Unbreakable cipher Is it possible to create an unbreakable cipher?

16. Unbreakable cipher Is it possible to create an unbreakable cipher? One-time pad  Plaintext: x 1 x 2 x 3... x n  Random string: b 1 b 2 b 3... b n  Ciphertext: y i = x i  b i Cryptanalisis? Applications?

17. One-Time Pad Keys Generate random sequence  Hardware generators Thermal noise from a semiconductor device Random fluctuations in disk sector latency times Etc.  Software generators Deterministic Initiated „randomly”  System clock  Elapsed time between keystrokes  Etc.

18. Pseudorandom Numbers Linear congruential generator  x i = ax i-1 + b (mod m)  Dangerous for cryptography! Blum-Blum-Shub generator  x i = x i-1 2 (mod n)  u i = x i (mod 2) Many others...