Math 418

Index of Hand-outs

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Date No. Title

12 Sep 11 01/02 Course Information

* Public Key Cryptography (2pp.)

* The Dancing Men

19 Sep 11 03 MAPLE homework instructions

* The Euclidean Algorithm

21 Sep 11 * The Extended Euclidean Algorithm: Examples 1 and 2 (2pp.)

* The Extended Euclidean Algorithm (Matrix Method) (2pp.)

* The Extended Euclidean Algorithm (Maple Program)

22 Sep 11 * Solving mx + ny = c and ax = b (mod m)

* The Chinese Remainder Theorem

26 Sep 11 * The Binary Power Method (2pp.)

28 Sep 11 * Cryptography and Group Theory

29 Sep 11 05/06 Basic facts about group elements (2pp.)

* Orders of elements mod 11

03 Oct 11 * Calculating the Order of a Group Element

06 Oct 11 * Generators of F_p^* (2pp.)

13 Oct 11 07 Quadratic residues

17 Oct 11 * Modular Square roots

19 Oct 11 * The Ring A_f

* Finite Fields (2pp.)

20 Oct 11 * Review of time estimates for algorithms

* The Definition of Cryptosystems

24 Oct 11 * The RSA Method (2pp.)

26 Oct 11 * The RSA Challenge

27 Oct 11 * DL-Cryptosystems

* History of DL-Cryptosystems

* DL-Cryptosystems: Examples (5pp.)

31 Oct 11 * Hashfunctions

02 Nov 11 * Attacks and their consequences (3pp.)

03 Nov 11 * Primality Tests (3pp.)

08 Probability Analysis of Primality Tests

09 Nov 11 * Elliptic Curves (2pp.)

* Elliptic Curves (Graphs)

* Elliptic Curves (Graphs)

14 Nov 11 09 Comments and Hints for Term Project

* Realistic Time/Space Estimates

* Elliptic Curves over Finite Fields

17 Nov 11 * Elliptic Curves: A small example

21 Nov 11 * Digital Signature (ECDSA)

23 Nov 11 * Pollard's p - 1 Method

24 Nov 11 * Lenstra's Factorization Method (2pp.)

28 Nov 11 * Pocklington's Primality Test

* The Goldwasser/Kilian EC Primality Test (2pp.)