1. 1 CIS 5371 Cryptography 1.Introduction

2. 2 Prerequisites for this course  Basic Mathematics, in particular Number Theory  Basic Probability Theory  Problem solving skills  Programming skills (for projects)

3. 3 Goals for the Introduction  Discuss the effectiveness & practicality of crypto.  Discuss the foundations of crypto.  Establish a mindset for developing crypto systems for Information Assurance.

4. 4 Cryptography vs Modern Cryptography  Pre 1970: The art of writing or solving codes  Post 1980: The science/technology of developing techniques for securing  digital information  digital transactions and  distributed computations  Usage:  Pre 1970: military, diplomatic services, intelligence.  Post 1980: most of us

5. 5 Modern Cryptography 1.Message Authentication, digital signatures 2.Secret Key exchange/distribution 3.Authentication protocols (for secure access) 4.e-commerce, e-government, e-auctions, e-voting and other e-applications. 5.Digital cash 6.Support system security 7.... and more

6. 6 The setting for Private Key encryption

7. The syntax of encryption  A key generation algorithm Gen:  A probabilistic algorithm that outputs a key k according to some distribution.  An encryption algorithm Enc  Takes as input a key k and a plaintext m and outputs a ciphertext c: c = Enc k (m).  A decryption algorithm Dec  Takes as input a key k and a ciphertext c and outputs a plaintext m’: m’ = Dec k (c).  Must have m’ = m. 7

8. 8 Kerckhoffs’ principle  “The cipher method must not be required to be secret, and it must be able to fall into the hands of the enemy without inconvenience.’’  Todays understanding  Security should not rely on the secrecy of the algorithms being used---indeed these algorithms should be public.  Open crypto design vs “security by obscurity”.

9. Attack Scenarios  Ciphertext-only attack (passive)  Known-plaintext attacks (passive)  Chosen-plaintext attack (active-adaptive)  Chosen-ciphertext attack (active-adaptive) Different applications of encryption may require the encryption scheme to be resilient to different types of attack. 9

10. Historical Ciphers and their Cryptanalysis  Ceasar’s cipher  a shift cipher that rotates letters  Mono-alphabetic substitution  uses a permutation of the alphabet, many more keys  Vigenere’s poly-alphabetic shift cipher  Multiple shift ciphers using a word.  Cryptanalysis based on  statistical pattern of the English language: the frequency of letters, digrams etc. 10

11. Basic principles of Modern Cryptography 1.Formulation of exact definitions 2.Reliance on precise assumptions 3.Rigorous Proofs of security 11

12. Principal 1 Formulation of exact definitions 1.Importance of design 2.Importance of usage 3.Importance of study 12

13. Examples for Principal 1 Question  An encryption scheme is secure if … 13

14. Examples for Principal 1 Tentative Answers 1.An encryption scheme is secure if no adversary can find the secret key when given a ciphertext. 2.An encryption scheme is secure if no adversary can find the plaintext that corresponds to a given ciphertext. 3.An encryption scheme is secure if no adversary can determine any character of the plaintext that corresponds to the ciphertext. 4.An encryption scheme is secure if no adversary can determine any meaningful information about the plaintext from the ciphertext. 14

15. Principal 1 A first answer An encryption scheme is secure if no adversary can compute any function of the plaintext from the ciphertext. 1.What is assumed to be the power of the adversary? 2.What is considered to be a break? A first definition of security: A cryptographic scheme for a given task is secure if no adversary of a specified power (e.g., an “efficient adversary”) can achieve a specific break. 15

16. Mathematics and the real world Models If a mathematical definition does not model appropriately the real world problem then the definition may be useless --- e.g., the adversarial power may be to weak, or the break may not may not be foreseen. Our arguments 1.Appeal to intuition 2.Proof of equivalence 3.Examples 16

17. Principal 2 Reliance on precise assumptions 1.Validation of the assumption  By their very nature assumptions/statements are not proven but conjectured... 2.Comparison of schemes  If one scheme makes a weaker assumption than another then the first is to be preferred... 3.Facilitation of proofs of security  If the security of a scheme cannot be proven unconditionally and must rely on an assumption then a mathematical proof that the construction is secure requires a precise definition of the statement. 17

18. Principal 3 Rigorous Proofs of security Reductionist approach: “Given assumption X is true, construction Y is secure according to the given definition. ” 18