Lecture 12: October 21, 2019
Reading: text, §10.2–10.3
Due: Lab 1, due October 18, 2019; Homework 2, due October 21, 2019
- Greetings and felicitations!
- Puzzle of the Day
- Symmetric Cryptography
- Polyalphabetic: Vigenère, f_{i}(a) = a + k_{i} mod n
- Cryptanalysis: first do index of coincidence to see if it is monoalphabetic or polyalphabetic, then Kasiski method.
- Problem: eliminate periodicity of key
- Long key generation
- Autokey cipher: key is keyword followed by plaintext or cipher text
- Running-key cipher: key is simply text; wedge is that (plaintext, key) letter pairs are not random (T/T, H/H, E/E, T/S, R/E, A/O, S/N, etc.)
- Perfect secrecy: when the probability of computing the plaintext message is the same whether or not you have the ciphertext; only cipher with perfect secrecy: one-time pads; C = AZPC; is that DOIT or DONT?
- 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)
- RSA
- Provides both authenticity and confidentiality
- Go through algorithm:
Idea: C = M^{e} mod n,
M = C^{d} 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 = M^{e} mod n =
2^{11} mod 35 = 2048 mod 35 = 18, and
M = C^{d} mod n = 18^{11} 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,
␢ (space) = 26.
Then: M = RE NA IS SA NC E␢ =
1704 1300 0818 1800 1302 0426
So: C = 1704^{71} mod 3233 = 3106;
… = 3106 0100 0931 2691 1984 2927