The Mathematics of Public-Key Cryptography, Lecture 20

November 23, 2000

Summary of material covered in lecture 20

• ECDSA
  • description of scheme
  • parameters and choice of elliptic curves (random curves over F_p and F_{2^m}, and Koblitz curves over F_{2^m}
• Full domain hash (FDH)
  • description of FDH using an arbitrary family F of trapdoor oneway permutations on {0,1}^k and a hash function with range {0,1}^k
  • proof that FDH is secure against a known key attack with respect to existential forgeries in the random oracle model, provided that it infeasible to invert f
  • discussion of the reduction: construction of an algorithm to invert f, given an algorithm that constructs forged signatures with a specified probability
  • preliminary analysis of success probability of inverting algorithm