This course explores the intersection of mathematics and cryptography, focusing on various cryptographic techniques and their applications. By the end of the course, learners will understand elliptic curve cryptography, Diffie-Hellman key agreement, pairing-based cryptography, fully homomorphic encryption, and lattice-based cryptography. The teaching method includes theoretical explanations, historical context, and real-world examples. This course is intended for individuals interested in cryptography, mathematics, computer science, and cybersecurity.
Mathematics and Cryptography - A Marriage of Convenience?
Overview
Syllabus
Intro
Life in the Age of the Coronavirus ...
Bad Haircuts in the Age of the Coronavirus
Health is the highest priority
Pictures and Stories
Working well together
Communication: Avoid Jargon
Community: the Ross Program
Computers: Doing the Right Thing?
Elliptic Curves
Elliptic Curve Cryptography (1980s)
IBM - they knew the law, and obeyed it
Being open to opportunities
Diffie-Hellman key agreement
XTR (Arjen Lenstra & Eric Verheul, 2000)
CEILIDH (Karl Rubin & A.S., 2003)
CEILIDH in the TV show NUMB3RS
Torus-Based Cryptography (Karl Rubin & A.S., 2003)
One-round 3-party key agreement (Antoine Joux, 2000)
Pairing-Based Cryptography
Cryptographic multilinear maps? (Dan Boneh & A.S., 2003)
One-round multiparty key agreement?
Grounds for pessimism, and grounds for optimism
One-round multi-party key agreement?
Working with others
Fully Homomorphic Encryption and Lattices
Communication is key
Get Curious, Not Furious
Relationships are negotiations
Listening
Alice's Adventures in Numberland
Kindness is a Superpower
We're all in the same boat
Taught by
TheIACR
