Elliptic Curves: Implementation

• Optimal Extension Fields
  • Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms (Dan Bailey, Christof Paar, Crypto '98)
  • Usage of Optimal Extension Fields for Elliptic Curve Cryptosystems (Tetsutaro Kobayashi, Kazumaro Aoki, Fumitaka Hoshino, Kunio Kobayashi and Hikaru Morita, August 1999)
  • Usage of Optimal Extension Fields for Elliptic Curve Cryptosystems ( Tetsutaro Kobayashi, Kazumaro Aoki, Fumitaka Hoshino, Kunio Kobayashi and Hikaru Morita, August 1999)
  • Fast Implementation of Elliptic Curve Arithmetic in GF(p^n) (Chae Hoon Lim and Hyo Sun Hwang, PKC '2000)
  • Public-Key Cryptography with Arbitrary Finite Fields (Daniel V. Bailey and Christof Paar, 2000)
• Overview and comparisons
  • Implementation Options for Finite Field Arithmetic for Elliptic Curve Cryptosystems ( Christof Paar, 1999)
  • Software Implementation of Elliptic Curve Cryptography Over Binary Fields (Darrel Hankerson, Julio Lopez Hernandez, Alfred Menezes, 2000)
• Efficient Algorithms for Elliptic Curve Cryptosystems (J. Guajardo, C. Paar, Crypto 97)
• Field Inversion and Point Halving Revisited (Kenny Fong, Darrel Hankerson, Julio López, Alfred Menezes, 2003)
• Koblitz curves
  • Improved Algorithms for Arithmetic on Anomalous Binary Curves (Jerome Solinas)
• Fast algorithms
  • Almost Inverse Algorithm
    • Fast Key Exchange with Elliptic Curve Systems (Richard Schroeppel, Hilarie Orman, Sean O'Malley, 1995)
  • Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms (Robert P. Gallant, Robert J. Lambert, and Scott A. Vanstone, CRYPTO 2001)
• Hyperelliptic Curves
  • Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves (Jan Pelzl and Thomas Wollinger and Jorge Guajardo and Christof Paar, eprint 2003/026)
• Link Collections
  • Elliptic Curves -- Galois Field Arithmetic (Rich Scroeppel)
    • Assembly code for GF multiplication on the Alpha

---

Cryptology Pointers by Helger Lipmaa
Got any suggestions or additional links? Mail to <helger.lipmaa>gmail.com
NB! If you find any broken links, please be kind and report them to me together with their current location!

(C) Helger Lipmaa 1997-2009.