---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/BasicRings/Integers/bibliography.html"
source: "https://docs.magma-maths.org/BasicRings/Integers/bibliography.md"
part: "Basic Rings"
chapter: "Ring of Integers"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Basic Rings", "source": "../index-basic-rings.md"}
  - {"title": "Ring of Integers", "source": "index-integers.md"}
prev: {"title": "Advanced Factorization Techniques: The Number Field Sieve", "source": "nfs.md"}
next: {"title": "Integer Residue Class Rings", "source": "../ResidueClassRings/index-residue-class-rings.md"}
---

# Bibliography

<a id="cite-ahohopcroftullman"></a>
- **[AHU74]** A.V. Aho, J.E. Hopcroft, and J.D. Ullman. *The Design and Analysis of Computer Algorithms*. Addison-Wesley, Reading, MA, 1974.
<a id="cite-atkinmorain"></a>
- **[AM93]** A. O. L. Atkin and F. Morain. Elliptic curves and primality proving. *Math. Comp.*, 61:29 – 68, 1993.
<a id="cite-brent80"></a>
- **[Bre80]** R. P. Brent. An improved Monte Carlo factorization algorithm. *BIT*, 20:176–184, 1980.
<a id="cite-brentteriele"></a>
- **[BtR92]** R. P. Brent and H. J. J te Riele. Factorizations of $a^n \pm 1$, $13 \le a < 100$. Technical Report, Centrum voor Wiskunde en Informatica, Amsterdam, 1992. URL:ftp://nimbus.anu.edu.au/pub/Brent.
<a id="cite-frankeetalt"></a>
- **[FKMW04]** J. Franke, T. Kleinjung, F. Morain, and T. Wirth. Proving the primality of very large numbers with fastECPP. In *Algorithmic number theory*, volume 3076 of Lecture Notes in Comput. Sci., pages 194–207. Springer, Berlin, 2004.
<a id="cite-knuth2"></a>
- **[Knu97]** Donald E. Knuth. *The Art of Computer Programming*. Volume 2. Addison Wesley, Reading, Massachusetts, 3rd edition, 1997.
<a id="cite-dodsonlenstra"></a>
- **[LD95]** Arjen K. Lenstra and Bruce Dodson. NFS with four large primes: An explosive experiment. In Don Coppersmith, editor, *Advances in cryptology—CRYPTO 1995*, volume 963 of LNCS, 372–385. Berlin, 1995. Springer.
<a id="cite-marsagliadiehard"></a>
- **[Mar95]** G. Marsaglia. DIEHARD: a battery of tests of randomness. http://stat.fsu.edu/pub/diehard/, 1995.
<a id="cite-marsaglia"></a>
- **[Mar00]** G. Marsaglia. The Monster, a random number generator with period over $10^{2857}$ times as long as the previously touted longest-period one. Preprint, 2000.
<a id="cite-marsaglia92"></a>
- **[Mar92]** George Marsaglia. The mathematics of random number generators. In *The unreasonable effectiveness of number theory (Orono, ME, 1991)*, volume 46 of Proc. Sympos. Appl. Math., pages 73–90. Amer. Math. Soc., Providence, RI, 1992. URL: [http://dx.doi.org/10.1090/psapm/046/1195842](http://dx.doi.org/10.1090/psapm/046/1195842).
<a id="cite-marsagliazaman"></a>
- **[MZ91]** George Marsaglia and Arif Zaman. A new class of random number generators. *Ann. Appl. Probab.*, 1(3):462–480, 1991.
<a id="cite-montgomery-thesis"></a>
- **[Mon92]** Peter Lawrence Montgomery. *An FFT Extension of the Elliptic Curve Method of Factorization*. PhD thesis, University of California, Los Angeles, 1992.
<a id="cite-murphy"></a>
- **[Mur99]** Brian Murphy. *Polynomial selection for the number field sieve integer factorisation algorithm*. PhD thesis, Oxford University, 1999. http://web.comlab.ox.ac.uk/oucl/work/richard.brent/ftp/Murphy-thesis.ps.gz.
<a id="cite-schoenhage-gcd"></a>
- **[Sch71]** Arnold Schönhage. Schnelle Berechnung von Kettenbruchentwicklungen. *Acta Informatica*, 1:139–144, 1971.
<a id="cite-sorenson2017strong"></a>
- **[SW17]** Jonathan Sorenson and Jonathan Webster. Strong Pseudoprimes to Twelve Prime Bases. *Mathematics of Computation*, 86(304):985–1003, 2017. [doi:10.1090/mcom/3134](https://doi.org/10.1090/mcom/3134).
<a id="cite-gathengerhard"></a>
- **[vzGG99]** Joachim von zur Gathen and Jürgen Gerhard. *Modern Computer Algebra*. Cambridge University Press, Cambridge, 1999.
<a id="cite-weber-gcd"></a>
- **[Web95]** Kenneth Weber. The Accelerated Integer GCD Algorithm. *ACM Transactions on Mathematical Software*, 21(1):111–122, 1995.