JHR's Elliptic Curve Cryptography page

MA478
Topics in Number Theory

MTRF 6, G220, Winter 2007-2008
John Rickert, Associate Professor of Mathematics
Office: G-215A, Crapo Hall
Phone: (812) 877-8473

e-mail: rickert@rose-hulman.edu

Recommended Text: Elliptic Curves: Number Theory and Cryptography by Lawrence Washington. He has a list of errata on his webpage.
For Tuesday, November 27: Work the modular arithmetic exercises. Turn these in Thursday.
For Thursday, November 29: Practice some congruences from the exercises passed out in class Tuesday. (These will not be collected as a set)
For Thursday, December 6: Turn in the groups, rings, and fields exercises.
The elliptic curve addition exercises are on line.
Monday, December 10: The morphisms worksheet is online.
For Thursday, December 13: Turn in the elliptic curve addition exercises.
For January 7, 2008: Study the elliptic curve E:y2 = x3-16x+16 modulo p, for several primes p. What can you discover? Are there any patterns? What conjectures can you make? What can you prove?
Consider the curve E over a field of size 9. What can &alpha2 be? Does changing this affect the structure of the group?

From Februrary 1, 2008: An HTML version of the ElGamal exercises in now available. The Elliptic Curve Cryptography Worksheet/Homework is due Thursday, February 7.
From Februrary 10, 2008: An amended HTML version of the ElGamal exercises in now available.
From Februrary 11, 2008: Version 3 of theHTML version of the ElGamal exercises in now available.
In this course we will be studying Algebra and algebraic number theory, with a concentration on the aspects that relate to modern cryptography.

Until recently, most methods of encrypting messages were essentially a simple matrix multiplication whose security lay in the fact that the elements of the matrix were unknown. In the late 1970s, Rivest, Shamir, and Adelman described a technique that took advantage of the fact that factoring integers is a hard problem. Their scheme uses the cyclic group generated using modular arithmetic. More recently, others have invented schemes using Elliptic curves to make use of groups that have more complicated structure.
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