NoteNextra-origin/content/CSE4303/CSE4303_L7.md

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