cover   Guide to
Elliptic Curve Cryptography

Darrel Hankerson, Alfred Menezes, and Scott Vanstone


The Guide was published in 2004. This page collects selected updates, but is clearly only a sampling of relevant material released since publication.

Pages 18 and 22. ECC2-109 claimed, April 2004. "Chris Monico, an assistant professor at Texas Tech University, and his team of mathematicians have successfully solved the Certicom Elliptic Curve Cryptography (ECC)2-109 Challenge. The effort required 2600 computers and took 17 months." See the announcement.
Page 21. Advances in Elliptic Curve Crytography by I. Blake, G. Seroussi, N. Smart (with contributions by D. Brown, A. W. Dent, E. Oswald, M. Joye, F. Vercauteren, P. Gaudry, F. Hess, S. Galbraith, and K. G. Paterson) is expected April 2005.
Page 60, below Algorithm 2.50. Techniques to enlarge the class of "suitable polynomials" are noted in: Field inversion and point halving revisited (Fong, Hankerson, López, and Menezes), Transactions on Computers 53(8):1047-1059, 2004. This also adds data related to pages 222-223.
Page 72. Normal basis arithmetic in software implementations is explored futher in:
  1. Arash Reyhani-Masoleh, Efficient algorithms and architectures for field multiplication using Gaussian normal bases, Technical Report CACR 2004-04, University of Waterloo, Canada, 2004.
  2. Haining Fan and Yiqi Dai, Two Software Normal Basis Multiplication Algorithms for GF(2n), Cryptology ePrint Archive, Report 2004/126, 2004,
  3. R. Dahab, D. Hankerson, F. Hu, M. Long, J. López and A. Menezes, Software Multiplication using Normal Bases, Technical Report CACR 2004-12, University of Waterloo, Canada, 2004.

Page 103, Algorithm 3.40. Steps 3 and 4 appear to require two field divisions. B. Poettering (on Sep 6, 2004) suggested the the following organization to eliminate a divsion. Let X0/Z0 and X1/Z1 be the x-coords of kP and (k+1)P, resp.
T = Z0*Z1
Z0 = Z0*x + X0
Z1 = Z1*x
X0 = X0*Z1
Z1 = (Z1 + X1)*Z0
Z0 = (x2 + y)*T + Z1
T = (T*x)-1
Z0 = Z0*T
X0 = X0*T
return (X0, y + (X0 + x)*Z0)

Page 285. Reference [144] appears in slightly abbreviated form in IEEE Transactions on Computers 53(8):1047-1059, 2004.
Page 295. Reference [318] appears in Topics in Cryptology - CT-RSA 2004, Lecture Notes in Computer Science 2964:366-386, 2004.
Guide to Elliptic Curve Cryptography / / Illustration by Helen D'Souza / Last updated on March 3, 2005