JHR's Elliptic Curve Cryptography page

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
My schedule this term.
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 Monday, December 7: Turn in the Modular arithmetic homework.
For Monday, December 14: Turn in the Group/Ring/Field homework.
For Monday, January 11: Turn in the Morphisms homework.

The Elliptic Curve Addition practice.
Exercises from the textbook: 4.3,4.4, 5.2,5.3,5.5.
Turn in exercises 4.3,4.4, 5.2,5.3,5.5, 6.2,6.4,6.6,6.7 by 5:00PM EST Thursday, Februrary 25, A.D. 2010.

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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