1. Modern Cryptographic Topics
Dimitri DeFigueiredo
University of California, Davis
Department of Computer Science

2. Overview
Security
Cryptography
Computer Security
Network Security

3. Historical Background
Encryption
Alice
Bob
Encrypt
Decrypt M C M’ K
Kerkhoffs’ Principle 1883

4. Time Line 300 – Caesar Cipher
1883 – Kerkhoffs “La Cryptographie Militaire”
1939 – Enigma
1975 – DES
1976 – Diffie-Hellman Asymmetric Encryption
1978 – RSA
1984 – Goldwasser Micali Provable Security

5. Modern Cryptology Cryptography and Cryptanalysis Goals: Encryption
Authentication
others (secret sharing, commitments, ZK)

6. Using a One-way function.
Motivation
How do we flip a coin over the phone?
Using a One-way function. x
f(x)
Easy
Hard
Do they exist?

7. Asymmetric Encryption
Diffie-Hellman 1976
Alice
Bob
Encrypt
Decrypt M C M’
Bob’s Public key
Bob’s Private Key

8. The man-in-the-middle attack
Playing chess:
man in the middle
Karpov
Kasparov

9. The Attack Model What does the adversary do?
What can the adversary do?
Computationally bounded/unbounded
Passive/Active
Has side information?
Give the adversary as much power as possible.

10. Raw RSA Encryption Setup: Choose 2 large primes: p, q
Calculate n = p  q
Randomly choose e ( e not divisible by (n) )
Calculate: d such that: d  e  1 mod (n)
Public key = (n,e)
Private key = (n,d)

11. Raw RSA Encryption Setup: Choose 2 large primes: 7, 17
Calculate n = 7  17 = 119
(n) = (p -1)(q -1) = 6  16 = 96
Randomly choose e = 5 ( 5 is not divisible by 96 )
Calculate: d such that: d  e  1 mod (n)
d = 77 (because 77  5 = 385 = 4  )
Public key = (119, 5) Private key = (119, 77)

12. Cd mod n = (Me)d mod n = M1 mod n
Raw RSA Encryption
Encryption:
C = Me mod n
Decryption
M = Cd mod n
because
Cd mod n = (Me)d mod n = M1 mod n

13. Raw RSA Encryption Example: Public key = (119, 5)
Private key = (119, 77)
(M must be smaller than n)
M = 19,
Encryption:
C = Me mod n = 195 mod 119 = 66
Decryption
M = Cd mod n = 6677 mod 119 = 19

14. Commitment schemes Back to fair coin flipping. Draft protocol:
1. A chooses random ba
2. B chooses random bb
3. AB: commitment( ba )
4. BA: bb
5. A : opens commitment.
6. Both A and B calculate (ba  bb)

15. Commitment Schemes Using RSA: Choose random bit of either 0 or 1.
Encrypt random value with public key. C = Eku(M)
Send ciphertext.
To open commitment decrypt.

16. Fair Coin Flipping Draft Protocol: assumes underlying PKI
RSA can be used as commitment
randomness needed!

17. Provable Security Precise definitions. Reduction based.
Builds adversaries using black box paradigm.
Example:
If adversary can cheat when flipping coin than we can use it to break RSA.

18. Zero Knowledge Proofs
Cut-and-choose paradigm. V P