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A Tour of NTL: Introduction

NTL is a high-performance, portable C++ library providing data structures and algorithms for arbitrary length integers; for vectors, matrices, and polynomials over the integers and over finite fields; and for arbitrary precision floating point arithmetic.

NTL provides high quality implementations of state-of-the-art algorithms for:

- arbitrary length integer arithmetic and arbitrary precision floating point arithmetic;
- polynomial arithmetic over the integers and finite fields including basic arithmetic, polynomial factorization, irreducibility testing, computation of minimal polynomials, traces, norms, and more;
- lattice basis reduction, including very robust and fast implementations of Schnorr-Euchner, block Korkin-Zolotarev reduction, and the new Schnorr-Horner pruning heuristic for block Korkin-Zolotarev;
- basic linear algebra over the integers, finite fields, and arbitrary precision floating point numbers.

NTL's polynomial arithmetic is one of the fastest available anywhere, and has been used to set "world records" for polynomial factorization and determining orders of elliptic curves.

NTL's lattice reduction code is also one of the best available anywhere, in terms of both speed and robustness, and one of the few implementations of block Korkin-Zolotarev reduction with the Schnorr-Horner pruning heuristic. It has been used to "crack" several cryptosystems.

NTL can be easily installed in a matter of minutes on just about any platform, including virtually any 32- or 64-bit machine running any flavor of Unix, as well as PCs running Windows 95, 98, or NT, and Macintoshes. NTL achieves this portability by avoiding esoteric C++ features, and by avoiding assembly code; it should therefore remain usable for years to come with little or no maintenance, even as processors and operating systems continue to change and evolve. However, NTL can be used in conjunction with GMP (the GNU Multi-Precision library) for enhanced performance.

NTL provides a clean and consistent interface to a large variety of classes representing mathematical objects. It provides a good environment for easily and quickly implementing new number-theoretic algorithms, without sacrificing performance.

NTL is written and maintained by Victor Shoup with some contributions made by others (see Acknowledgements).

## Legalistic Nonsense

NTL is free software, and may be used according to the terms of the GNU General Public License.

[the precise licensing information of NTL]

[more information about the GNU General Public License]