Applied arithmetic geometry
Date
2019-08-12
Authors
Dr. Ambrus, Pal
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
The aim of this lecture series is to introduce some methods of arithmetic geometry which
are applied in cryptographic research. Cryptography, including more sophisticated
versions such as elliptic curve cryptography, allows for efficient protocols for information
security, and is widely used in the banking sector including mobile money transfers, an
industry in which Africa is a world leader. The methods presented can be used by African
research groups to tackle a range of problems arising in technological challenges relevant
to the African development context. Arithmetic geometry is a rather modern, highly
prestigious and very developed area of pure mathematics, developed originally for
studying Diophantine equations. I has very efficient methods to count points on algebraic
varieties over finite fields which is closely related to the original motivating problem of
finding rational points on varieties over number fields, a geometric reformulation of
Diophantine equations. The former problem is very important in cryptography and related
areas of secure communication, network building and hash functions. The lecture series
will cover the necessary background on cryptography and point counting, and will
introduce such tools as p-adic numbers, differential forms and Monsky-Washnitzer
cohomology, from the ground up.
Description
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya.
Keywords
Arithmetic geometry, cryptography, Monsky-Washnitzer cohomology