The Mathematics of Public-Key Cryptography, Lecture 17

November 14, 2000

Summary of material covered in lecture 17

• ElGamal public-key cryptosystem in Z_p*
  • find p so that p and (p-1)/2 are both prime
  • how to find a primitive element mod p
  • complexity of encryption and decryption
  • message expansion = 2
• elliptic curve variants of ElGamal
  • choosing a suitable curve E over Z_p (p prime)
  • problem of deterministically generating points on the curve E
  • message expansion = 4
  • more efficient variations
• computing a multiple "a" of an elliptic curve point alpha
  • double-and-add algorithm
  • efficiency of subtracting points on an elliptic curve
  • signed digit representation
  • double-and-(add or subtract) algorithm