projects / apple / security.git / blame
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| b1ab9ed8 A |
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 |