Security/libsecurity_cryptkit/lib/CurveParamDocs/README

   1 TOOLS for Apple-CryptKit curve generation/testing.
   2 24 Apr 2001 REC
   3
   4 The state-of-the-art in ECC (elliptic-curve cryptography)
   5 is in a well known mode of imperfection.  For example,
   6 it is very easy to generate CM (complex-multiplication)
   7 curves, with known order and parameters; yet, it is suspected
   8 by some (though unproven in any sense of rigor)
   9 that better security accrues if curves are entirely
  10 "random" in the sense of random base prime p, and random (a,b)
  11 under minimal constraints such as prime curve order, etc.
  12 Thus the collection of this Directory is a potpourri of
  13 various tools, including a Schoof implementation (schoof.c,
  14 schoofs.c) for arbitrary curves.  As expected, said implementation
  15 is very slow, yet we have used it for some of the current
  16 CryptKit curves, while for other curves we have used the
  17 fast CM methods, and for yet other curves we have borrowed
  18 recommended parameters from other investigators.
  19
  20 Contained in this Directory are various C sources:
  21
  22 * curvegen.c, curvegenFEE.c
  23   Utility for generating CM curves, links to other sources
  24   as shown in comment atop source.
  25
  26 * factor.c
  27   Utility for factoring such as curve orders;
  28   see comment atop source.
  29
  30 * giants.c, ellproj.c, fmodule.c, tools.c
  31   Number-theoretical library sources, having standard and
  32   some ECC-specific tools.
  33
  34 * schoof.c, shoofs.c
  35   Curve-order finder, using the celebratd Schoof algorithm
  36   When run, you input p, a, b (Weierstrass parameterization)
  37   and out comes the curve order, sometimes after a very long
  38   wait.  The source schoofs.c is a "sieving Schoof" method
  39   as explained in the References below, for finding curves
  40   of prime-or-nearly-prime order (along with the same constraint
  41   for twists).
  42
  43 together with Mathematica sources:
  44
  45 * curverecords.nb
  46   A program to test current CryptKit points/orders.
  47
  48 * FEED affine.nb, FEEDsansY.nb
  49   Programs for testing FEED, in particular the integrity of
  50   any choice for x1Minus (a coordinate for the twist curve).
  51
  52 References
  53
  54 Crandall R and Pomerance C, "Prime numbers: a computational perspective," Springer-Verlag, 2001.
  55
  56 Crandall, R. E., U.S. Patents #5159632 (1992), #5271061 (1993),
  57     #5463690 (1994), "Method and apparatus for public key exchange in
  58     a cryptographic system."
  59
  60 Crandall, R. E. 1996 U. S. Patent #5581616, "Method and apparatus
  61     for Digital Signature Authentication."
  62