On cyclotomic primality tests
In 1980, L. Adleman, C. Pomerance, and R. Rumely invented the first cyclotomicprimality test, and shortly after, in 1981, a simplified and more efficient versionwas presented by H.W. Lenstra for the Bourbaki Seminar. Later, in 2008, ReneSchoof presented an updated version of Lenstra's primality...
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ndltd-UTENN-oai-trace.tennessee.edu-utk_gradthes-21512011-12-13T16:16:20Z On cyclotomic primality tests Boucher, Thomas Francis In 1980, L. Adleman, C. Pomerance, and R. Rumely invented the first cyclotomicprimality test, and shortly after, in 1981, a simplified and more efficient versionwas presented by H.W. Lenstra for the Bourbaki Seminar. Later, in 2008, ReneSchoof presented an updated version of Lenstra's primality test. This thesis presents adetailed description of the cyclotomic primality test as described by Schoof, along withsuggestions for implementation. The cornerstone of the test is a prime congruencerelation similar to Fermat's little theorem" that involves Gauss or Jacobi sumscalculated over cyclotomic fields. The algorithm runs in very nearly polynomial time.This primality test is currently one of the most computationally efficient tests and isused by default for primality proving by the open source mathematics systems Sageand PARI/GP. It can quickly test numbers with thousands of decimal digits. 2011-08-01 text application/pdf http://trace.tennessee.edu/utk_gradthes/949 Masters Theses Trace: Tennessee Research and Creative Exchange Gauss sums cyclotomic fields primality testing Number Theory |
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Gauss sums cyclotomic fields primality testing Number Theory |
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Gauss sums cyclotomic fields primality testing Number Theory Boucher, Thomas Francis On cyclotomic primality tests |
| description |
In 1980, L. Adleman, C. Pomerance, and R. Rumely invented the first cyclotomicprimality test, and shortly after, in 1981, a simplified and more efficient versionwas presented by H.W. Lenstra for the Bourbaki Seminar. Later, in 2008, ReneSchoof presented an updated version of Lenstra's primality test. This thesis presents adetailed description of the cyclotomic primality test as described by Schoof, along withsuggestions for implementation. The cornerstone of the test is a prime congruencerelation similar to Fermat's little theorem" that involves Gauss or Jacobi sumscalculated over cyclotomic fields. The algorithm runs in very nearly polynomial time.This primality test is currently one of the most computationally efficient tests and isused by default for primality proving by the open source mathematics systems Sageand PARI/GP. It can quickly test numbers with thousands of decimal digits. |
| author |
Boucher, Thomas Francis |
| author_facet |
Boucher, Thomas Francis |
| author_sort |
Boucher, Thomas Francis |
| title |
On cyclotomic primality tests |
| title_short |
On cyclotomic primality tests |
| title_full |
On cyclotomic primality tests |
| title_fullStr |
On cyclotomic primality tests |
| title_full_unstemmed |
On cyclotomic primality tests |
| title_sort |
on cyclotomic primality tests |
| publisher |
Trace: Tennessee Research and Creative Exchange |
| publishDate |
2011 |
| url |
http://trace.tennessee.edu/utk_gradthes/949 |
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AT boucherthomasfrancis oncyclotomicprimalitytests |
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