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Be sure to check back, because this may change during the semester.
All chapter references are to the text An Introduction to Mathematical Cryptography by Hoffstein, Pipher, and Silverman. We've already discussed some of the topics in the text during Math 202 last fall, so we can skip around a bit in the book.
For Friday January 27
Section 1.3 Modular Arithmetic
Focus on:
- How the notation differs slightly from last fall
- Section 1.3.2 The Fast Powering Algorithm
For Monday January 30
Section 1.4 Prime Numbers, Unique Factorization, and Finite Fields
1.5 Powers and Primitive Roots in Finite Fields
Focus on:
- Theorem 1.20 The Fundamental Theorem of Arithmetic
- Theorem 1.24 Fermat's Little Theorem
- Theorem 1.30 The Primitive Root Theorem
For Wednesday February 1
Section 1.7 Symmetric and Asymmetric Ciphers
2.3 Diffie-Hellman Key Exchange
Focus on:
- Notation for symmetric ciphers in Section 1.7.1 and asymmetric ciphers in Section 1.7.6
- The difference between the Discrete Log Problem (DLP) and the Diffie-Hellman Problem (DHP)
- Proposition 2.10 relating the difficulty of breaking Elgamal to the DHP
For Friday February 3
Section 2.4 The Elgamal Public Key Cryptosystem
2.5 An Overview of the Theory of Groups
Focus on:
- Review Proposition 2.10
- Definition of a group
- Proposition 2.12 on the order of an element in a finite group
For Monday February 6
Section 2.5 An Overview of the Theory of Groups
Focus on:
- Review topics from Friday
- Proposition 2.13 Lagrange's Theorem
For Wednesday February 8
Section 2.6 How Hard is the Discrete Logarithm Problem?
Focus on:
- Definition of order notation
- Proposition 2.14
For Friday February 10
Section 2.6 How Hard is the Discrete Logarithm Problem?
Focus on:
- Definitions of polynomial, exponential, and subexponential time algorithms
For Monday February 13
Section 2.7 A Collision Algorithm for the DLP
Focus on:
- Proposition 2.19 Trivial Bound for DLP
- Proposition 2.21 Shank's Babystep-Giantstep Algorithm
For Wednesday February 15
Section 2.8 The Chinese Remainder Theorem
Focus on:
- Theorem 2.24 Chinese Remainder Theorem
- Example 2.25 for solving simultaneous congruences
For Friday February 17
Section 2.9 The Pohlig-Hellman Algorithm
Focus on:
- Theorem 2.31 Pohlig-Hellman Algorithm for solving the DLP
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