### Summer 2017

• Syllabus
• Presentations:
1. Chinese Remainder Theorem – Rocca ✓
2. Euler’s $$\phi$$-Function and Euler’s Theorem ✓
3. Pseudoprimes, Miller’s Test, Theorem 6.8, Rabin’s Probabilistic Test (Theorem 6.11) – D. Ciskowski ✓
4. Mersenne Primes, Lucas-Lehmer Test – K. Ciskowski ✓
5. Lucas’s Converse to Fermat’s Little (Theorem 9.18) and Corollary 9.18.1 – D. Cook ✓
6. Theorem 9.19 and Big O-Notation – Rocca ✓
7. Pocklington’s and Proth’s Primality Tests – D. Ciskowski ✓
8. Sections 11.1-11.3 – Rocca ✓
9. Euler Pseudoprimes, Solovay-Strassen Probabilistic Test – K. Ciskowski ✓
10. Fermat Factorization – D. Cook
11. Pollard’s Rho Factorization Method – D. Ciskowski
12. Continued Fractions and theorem 12.8 – Rocca ✓
13. Theorem 12.7 – K. Ciskowski ✓
14. $$k^{th}$$-Convergent, Theorem 12.9 – D. Cook ✓
15. Theorem 12.15 – Rocca
16. Theorem 12.24 (including Lemma 12.6), Continued Fraction Factorization – D. Ciskowski
17. Rabin Cryptosystem (p. 329 and exercise 49 in section 11.1) – K. Ciskowski
18. Knapsack Problem and Super Increasing Sequences (pp. 331-333) – Rocca
19. Knapsack Ciphers (pp. 334-336) – D. Cook
20. Electronic Poker – Rocca
21. El Gamal Cryptosystem – Rocca
• Programing Assignments: These are listed on CoCalc.com
• Text Exercises: Do 8 of the following
• p.170 15 and 19
• p. 170 27-29 (use the result from #19, change periods to 23, 27, and 31 (why?))
• ???