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WEEK OF |
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SECTIONS |
TOPICS |
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Sep 6
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2.1 |
An overview of the course. Divisibility. |
| 1 |
Sep 10-14 |
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2.1-2.2 |
Divisibility. Primes. |
| 2 |
Sep 17-21 |
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2.3-2.4 |
Unique factorization. Elementary factoring
methods. |
| 3 |
Sep 24-28 |
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2.5-2.6 |
GCD and LCM. Linear Diophantine equations. |
| 4 |
Oct 1-5 |
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3.1-3.3 |
Congruences. Inverses mod p. Chinese remainder
theorem. |
| 5 |
Oct 8-12 |
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4.1-4.4 |
Fermat's theorem. Euler's Phi function. Euler's
theorem. Lagrange's theorem. |
| 6 |
Oct 15-19 |
midterm 1; assg. 1 due |
5.1 |
Classical cryptosystems. |
| 7 |
Oct 22-26 |
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5.2-5.3 |
Public-Key cryptography. The RSA scheme. |
| 8 |
Oct 29-Nov 2
|
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6.1, 6.3-6.4 |
Pseudoprimes and Carmichel numbers. Pollard's
p-1 and rho factorization methods. |
| 9 |
Nov 5-9 |
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7.1-7.4 |
Order. Discrete logarithm. Lucas-Lehmer test. |
| 10 |
Nov 12-16 |
midterm 2 |
8.1, 10.1 |
ElGamal cryptosystem. Identification schemes. |
| 11 |
Nov 19-23 |
assg. 2 due |
8.2, 9.1 |
Signature schemes. Quadratic residues. |
| 12 |
Nov 26-30
|
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17.1-17.3 or 12.2 |
Quadratic reciprocity law or quadratic sieve.
Review. |