CO 789: Topics in Cryptography
Pairing Based Cryptography
Winter 2007
Handouts
Lecture summaries
The lecture notes above are presented as a coherent whole instead
of a series of individual lectures. What follows is a rough outline of
which topics in the notes were covered on which days. Note that the
order of topics here differs from that in the written notes. Contents
of future lectures are estimates and are subject to change.
- January 4: Lattices and elliptic curves
- January 9: Divisors
- January 11: Elliptic functions
- January 16: Linear systems
- January 18: Riemann-Roch theorem
- January 23: Elliptic curve group law
- January 25: Definition of Weil pairing
- January 30: Properties of Weil and Tate pairings
- February 1: Pairing implementations and protocols
- February 6: Runtime analysis of DLOG attacks
- February 8: Embedding degree and supersingular curves
- February 13: Ordinary curves with small embedding degree
- February 15: Complex multiplication method
- February 27: j-Invariants and isomorphism
- March 1: Calculating the j-invariant
- March 6: Degree of the j-invariant for CM curves
- March 8: Protocols for identity based encryption