Lecture 19 Outline (May 11, 2015)
Assignment: Homework 3, due May 20, 2015
- Greetings and felicitations!
- Product ciphers: DES, AES
- Public-Key Cryptography
- Basic idea: 2 keys, one private, one public
- Cryptosystem must satisfy:
- Given public key, computationally infeasible to get private key;
- Cipher withstands chosen plaintext attack;
- Encryption, decryption computationally feasible (note: commutativity not required)
- Benefits: can give confidentiality or authentication or both
- Use of public key cryptosystem
- Normally used as key interchange system to exchange secret keys (cheap)
- Then use secret key system (too expensive to use public key cryptosystem for this)
- Provides both authenticity and confidentiality
- Go through algorithm:
Idea: C = Me mod n, M = Cd mod n, with ed mod φ(n) = 1
Public key is (e, n); private key is d. Choose n = pq; then φ(n) = (p−1)(q−1).
- Example: p = 5, q = 7; then n = 35, φ(n) = (5−1)(7−1) = 24. Pick d = 11. Then ed mod φ(n) = 1,
so e = 11
To encipher 2, C = Me mod n = 211 mod 35 = 2048 mod 35 = 18, and M = Cd mod n = 1811 mod 35 = 2.
- Example: p = 53, q = 61; then n = 3233, φ(n) = (53−1)(61−1) = 3120. Pick d = 791. Then e = 71
To encipher M = RENAISSANCE, use the mapping A = 00, B = 01, ..., Z = 25, b̸ = 26.
Then: M = RE NA IS SA NC Eb̸ = 1704 1300 0818 1800 1302 0426
So: C = (1704)71 mod 3233 = 3106 … = 3106 0100 0931 2691 1984 2927
- Cryptographic Checksums
- Function y = h(x): easy to compute y given x; computationally infeasible to compute x given y
- Variant: given x and y, computationally infeasible to find a second x′ such that y = h(x′)
- Keyed vs. keyless