Lecture 17: May 5, 2021
Reading: , §10.2–10.4
Due: Lab 2, due May 5, 2021 (Note new due date); Homework 3, due May 10, 2021 (Note new due date)
- 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)
- El Gamal
- Provides confidentility; there is a corresponding algorithm for authenticity
- Based on discrete log problem
- RSA
- Provides both authenticity and confidentiality
- Based on difficulty of computing totient, φ(n) when n is difficult to factor
- Elliptic curve cryptography
- Works for any cryptosystem depending on discrete log problem
- Example: Elliptic curve El Gamal
- Selection of curves
- 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
- Digital Signatures
- Judge can confirm, to the limits of technology, that claimed signer did sign message
- RSA digital signatures: sign, then encipher, then sign