The Mathematics of Public-Key Cryptography, Lecture 4

September 21, 2000

Reference

• read section 4.5 of the textbook for background

Summary of material covered in lecture 4

• Monte Carlo algorithms
  • yes-biased algorithm
  • error probability
• number theory background
  • Zp* is cyclic if p is prime
  • primitive elements in Zp*
  • quadratic residues modulo p (p prime)
  • Euler's criterion
  • Legendre symbols
  • Jacobi symbols
    • properties of Jacobi symbols (quadratic residuosity)
    • algorithm to compute Jacobi symbols
• Solovay-Strassen algorithm
  • complexity
  • error probability