The Mathematics of Public-Key Cryptography, Lecture 16

November 9, 2000

Summary of material covered in lecture 16

• elliptic curve groups
  • the group operation for an elliptic curve over the reals (geometric description)
  • finding points on an elliptic curve over Z_p
  • formula for the number of points on an elliptic curve over Z_p
  • Hasse's bound on the number of points on an ellictic curve over Z_p
  • structure of elliptic curve groups over Z_p
• review of Diffie-Hellman key agreement over an arbitrary group
• introduction to the ElGamal public-key cryptosystem as a variant of Diffie-Hellman key agreement