fix errors and update news

content/CSE4303/CSE4303_L7.md

@@ -0,0 +1,65 @@
+# CSE4303 Introduction to Computer Security (Lecture 7)
+
+## Cyptography in Symmetric Systems
+
+### Symmetric systems
+
+Symmetric (shared-key) encryption
+
+- Classical techniques
+- Computer-aided techniques
+- Formal reasoning
+- Realizations:
+  - Stream ciphers
+  - Block ciphers
+
+#### Stream ciphers
+
+1. Operate on PT one bit at a time (usually), as a bit "stream"
+2. Generate arbitrarily long keystream on demand
+
+Security abstraction:
+
+1. XOR transfers randomness of keystream to randomness of CT regardless of PT’s content
+2. Security depends on G being “practically” indistinguishable from random string and “practically” unpredictable
+3. Idea: shouldn’t be able to predict next bit of generator given all bits seen so far
+
+Keystream $G(k)$
+
+- Idea: shouldn’t be able to predict next bit of generator given all bits seen so far
+- Strategies and challenges: many!
+- Idea that doesn’t quite work: Linear Feedback Shift Register (LFSR)
+  - Choice of feedback: by algebra
+  - Pro: fast, statistically close to random
+  - Problem: susceptible to cryptanalysis (b/c linear)
+  - LFSR-based
+- Modifications to basic LFSR:
+  - Use non-linear combo of multiple LFSRs
+  - Use controlled clocking (e.g. only cycle the LFSR when another LFSR outputs a 1)
+  - Etc.
+- Others: mod arithmetic-based, other algebraic constructions
+
+#### Block ciphers
+
+1. Operate on PT one block at a time
+2. Use same key for multiple blocks (with caveats)
+3. Chaining modes intertwine successive blocks of CT (or not)
+
+View cipher as a Pseudo-Random Permutation (PRP)
+
+- PRP defined over $(K, X)$:
+
+$$
+E: K \times X \to X
+$$
+
+such that:
+
+1. There exists an “efficient” deterministic algorithm to evaluate $E(k,x)$.
+2. The function $E( k, \cdot )$ is one-to-one.
+3. There exists an “efficient” inversion algorithm $D(k,y)$.
+
+- i.e. a PRF that is an invertible 1-to-1 mapping from message space to
+message space
+
+