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M478
Topics in Number Theory
Elliptic Curve Cryptography
MTRF 3 CL-119 Winter 2016-17
Dr. Rickert
(G-215A, ext. 8473, Box 141)
In this course we will be studying the Algebra and algebraic number theory underlying elliptic curve 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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