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