| 1 | <html> |
|---|
| 2 | <head> |
|---|
| 3 | <title> |
|---|
| 4 | A Tour of NTL: Introduction </title> |
|---|
| 5 | </head> |
|---|
| 6 | |
|---|
| 7 | <body bgcolor="#fff9e6"> |
|---|
| 8 | |
|---|
| 9 | <center> |
|---|
| 10 | <img src="arrow1.gif" alt="[Previous]" align=bottom> |
|---|
| 11 | <a href="tour.html"><img src="arrow2.gif" alt="[Up]" align=bottom></a> |
|---|
| 12 | <a href="tour-examples.html"> <img src="arrow3.gif" alt="[Next]" align=bottom></a> |
|---|
| 13 | </center> |
|---|
| 14 | |
|---|
| 15 | |
|---|
| 16 | <h1> |
|---|
| 17 | <p align=center> |
|---|
| 18 | A Tour of NTL: Introduction |
|---|
| 19 | </p> |
|---|
| 20 | </h1> |
|---|
| 21 | |
|---|
| 22 | <p> <hr> <p> |
|---|
| 23 | |
|---|
| 24 | |
|---|
| 25 | <p> |
|---|
| 26 | NTL is a high-performance, portable C++ library providing |
|---|
| 27 | data structures and algorithms |
|---|
| 28 | for arbitrary length integers; |
|---|
| 29 | for vectors, matrices, and polynomials over the integers and over |
|---|
| 30 | finite fields; and for arbitrary precision floating point arithmetic. |
|---|
| 31 | |
|---|
| 32 | <p> |
|---|
| 33 | NTL provides high quality implementations of state-of-the-art |
|---|
| 34 | algorithms for: |
|---|
| 35 | |
|---|
| 36 | <ul> |
|---|
| 37 | |
|---|
| 38 | <li> |
|---|
| 39 | arbitrary length integer arithmetic and arbitrary precision |
|---|
| 40 | floating point arithmetic; |
|---|
| 41 | |
|---|
| 42 | <li> |
|---|
| 43 | polynomial arithmetic over the integers and finite fields |
|---|
| 44 | including basic arithmetic, polynomial factorization, |
|---|
| 45 | irreducibility testing, |
|---|
| 46 | computation |
|---|
| 47 | of minimal polynomials, traces, norms, and more; |
|---|
| 48 | |
|---|
| 49 | <li> |
|---|
| 50 | lattice basis reduction, including very robust and fast implementations |
|---|
| 51 | of Schnorr-Euchner, block Korkin-Zolotarev reduction, |
|---|
| 52 | and the new Schnorr-Horner pruning heuristic for |
|---|
| 53 | block Korkin-Zolotarev; |
|---|
| 54 | |
|---|
| 55 | <li> |
|---|
| 56 | basic linear algebra over the integers, |
|---|
| 57 | finite fields, and arbitrary precision |
|---|
| 58 | floating point numbers. |
|---|
| 59 | |
|---|
| 60 | </ul> |
|---|
| 61 | |
|---|
| 62 | <p> |
|---|
| 63 | NTL's polynomial arithmetic is one of the fastest available anywhere, |
|---|
| 64 | and has been used to set "world records" for polynomial factorization |
|---|
| 65 | and determining orders of elliptic curves. |
|---|
| 66 | |
|---|
| 67 | |
|---|
| 68 | <p> |
|---|
| 69 | NTL's lattice reduction code is also one of the best available anywhere, |
|---|
| 70 | in terms of both speed and robustness, and one of the few |
|---|
| 71 | implementations of |
|---|
| 72 | block Korkin-Zolotarev reduction with the Schnorr-Horner pruning heuristic. |
|---|
| 73 | It has been used to "crack" several cryptosystems. |
|---|
| 74 | |
|---|
| 75 | |
|---|
| 76 | <p> |
|---|
| 77 | NTL can be easily installed in a matter of minutes |
|---|
| 78 | on just about any platform, |
|---|
| 79 | including virtually any 32- or 64-bit machine running |
|---|
| 80 | any flavor of Unix, |
|---|
| 81 | as well as PCs running Windows 95, 98, or NT, and Macintoshes. |
|---|
| 82 | NTL achieves this portability by avoiding esoteric C++ features, |
|---|
| 83 | and by avoiding assembly code; it should therefore remain usable |
|---|
| 84 | for years to come with little or no maintenance, even as |
|---|
| 85 | processors and operating systems continue to change and evolve. |
|---|
| 86 | However, NTL can be used in conjunction with |
|---|
| 87 | <a href="tour-gmp.html">GMP (the GNU Multi-Precision library)</a> |
|---|
| 88 | for enhanced performance. |
|---|
| 89 | NTL can also be used in conjunction with the |
|---|
| 90 | <a href="tour-gf2x.html"><tt>gf2x</tt></a> library for faster |
|---|
| 91 | arithmetic of large degree polynomials over <i>GF(2)</i>. |
|---|
| 92 | |
|---|
| 93 | |
|---|
| 94 | <p> |
|---|
| 95 | NTL provides a clean and consistent interface to |
|---|
| 96 | a large variety of classes representing mathematical objects. |
|---|
| 97 | It provides a good environment for easily |
|---|
| 98 | and quickly implementing new |
|---|
| 99 | number-theoretic algorithms, <em>without sacrificing performance</em>. |
|---|
| 100 | |
|---|
| 101 | <p> |
|---|
| 102 | NTL is written and maintained by |
|---|
| 103 | <a href="http://www.shoup.net">Victor Shoup</a> |
|---|
| 104 | with some contributions made by others |
|---|
| 105 | (see <a href="tour-ack.html">Acknowledgements</a>). |
|---|
| 106 | |
|---|
| 107 | <p> |
|---|
| 108 | |
|---|
| 109 | <h2> |
|---|
| 110 | Legalistic Nonsense |
|---|
| 111 | </p> |
|---|
| 112 | </h2> |
|---|
| 113 | <p> |
|---|
| 114 | NTL is <i>free software</i>, and may be used according to |
|---|
| 115 | the terms of the GNU General Public License. |
|---|
| 116 | <p> |
|---|
| 117 | <a href="copying.txt">[the precise licensing information of NTL]</a> |
|---|
| 118 | <p> |
|---|
| 119 | <a href="http://www.gnu.org">[more information |
|---|
| 120 | about the GNU General Public License]</a> |
|---|
| 121 | |
|---|
| 122 | <p> |
|---|
| 123 | |
|---|
| 124 | <center> |
|---|
| 125 | <img src="arrow1.gif" alt="[Previous]" align=bottom> |
|---|
| 126 | <a href="tour.html"><img src="arrow2.gif" alt="[Up]" align=bottom></a> |
|---|
| 127 | <a href="tour-examples.html"> <img src="arrow3.gif" alt="[Next]" align=bottom></a> |
|---|
| 128 | </center> |
|---|
| 129 | |
|---|
| 130 | </body> |
|---|
| 131 | </html> |
|---|
