X-Git-Url: https://git.saurik.com/apple/security.git/blobdiff_plain/80e2389990082500d76eb566d4946be3e786c3ef..d8f41ccd20de16f8ebe2ccc84d47bf1cb2b26bbb:/libsecurity_cryptkit/lib/CurveParamDocs/README

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-TOOLS for Apple-CryptKit curve generation/testing.
-24 Apr 2001 REC
-
-The state-of-the-art in ECC (elliptic-curve cryptography)
-is in a well known mode of imperfection.  For example,
-it is very easy to generate CM (complex-multiplication)
-curves, with known order and parameters; yet, it is suspected
-by some (though unproven in any sense of rigor)
-that better security accrues if curves are entirely
-"random" in the sense of random base prime p, and random (a,b)
-under minimal constraints such as prime curve order, etc.
-Thus the collection of this Directory is a potpourri of
-various tools, including a Schoof implementation (schoof.c, 
-schoofs.c) for arbitrary curves.  As expected, said implementation
-is very slow, yet we have used it for some of the current
-CryptKit curves, while for other curves we have used the
-fast CM methods, and for yet other curves we have borrowed
-recommended parameters from other investigators.
-
-Contained in this Directory are various C sources:
-
-* curvegen.c, curvegenFEE.c
-  Utility for generating CM curves, links to other sources
-  as shown in comment atop source.
-
-* factor.c
-  Utility for factoring such as curve orders;
-  see comment atop source.
-
-* giants.c, ellproj.c, fmodule.c, tools.c
-  Number-theoretical library sources, having standard and
-  some ECC-specific tools.
-
-* schoof.c, shoofs.c
-  Curve-order finder, using the celebratd Schoof algorithm
-  When run, you input p, a, b (Weierstrass parameterization)
-  and out comes the curve order, sometimes after a very long
-  wait.  The source schoofs.c is a "sieving Schoof" method
-  as explained in the References below, for finding curves
-  of prime-or-nearly-prime order (along with the same constraint
-  for twists).
-
-together with Mathematica sources:
-
-* curverecords.nb
-  A program to test current CryptKit points/orders.
-
-* FEED affine.nb, FEEDsansY.nb
-  Programs for testing FEED, in particular the integrity of
-  any choice for x1Minus (a coordinate for the twist curve).
-
-References
-
-Crandall R and Pomerance C, "Prime numbers: a computational perspective," Springer-Verlag, 2001.
-
-Crandall, R. E., U.S. Patents #5159632 (1992), #5271061 (1993),
-    #5463690 (1994), "Method and apparatus for public key exchange in 
-    a cryptographic system."
-
-Crandall, R. E. 1996 U. S. Patent #5581616, "Method and apparatus
-    for Digital Signature Authentication."
-