{{위키데이터 속성 추적}}
'''계산수론'''(computational number theory)은 [[수학]]과 [[컴퓨터 과학]]에서 '''알고리즘 수론'''(algorithmic number theory)으로도 알려진 것으로, [[소수판별법]] 및 [[소인수분해]]를 위한 알고리즘, [[디오판토스 방정식]]의 해 찾기 등 수 이론 및 산술 기하학의 문제를 조사하고 해결하기 위한 계산 방법에 대한 연구이다. 산술 기하학의 명시적 방법이다. 계산수론은 [[RSA 암호|RSA]], [[타원곡선 암호]] 및 [[양자 후 암호]]를 포함한 암호학에 적용되며 리만 가설, [[버치-스위너턴다이어 추측]], [[Abc 추측]], [[모듈러성 정리]], 사토-테이트(Sato-Tate) 추측, [[랭글랜즈 프로그램]]의 명시적 측면 등에 응용된다.{{r|pcm}}{{r|bachshallit}}{{r|cohen}}

== 소프트웨어 패키지 ==
* [[마그마 (컴퓨터 대수학 시스템)]]
* [[SageMath]]
* [[Fast Library for Number Theory]]

== 참고 문헌 ==
*{{서적 인용
| author1   = Eric Bach | author1-link = Eric Bach
| author2   = Jeffrey Shallit | author2-link = Jeffrey Shallit
| title     = Algorithmic Number Theory, Volume 1: Efficient Algorithms
| publisher = MIT Press
| year      = 1996
| isbn      = 0-262-02405-5
| url       = https://cs.uwaterloo.ca/~shallit/ant.html
}}

*{{서적 인용
| author     = David M. Bressoud
| authorlink = David Bressoud
| title      = Factorisation and Primality Testing
| publisher  = Springer-Verlag
| year       = 1989
| isbn       = 0-387-97040-1
| url-access = registration
| url        = https://archive.org/details/factorizationpri0000bres
}}

* {{서적 인용
| editor1   = Joe P. Buhler | editor1-link = Joe P. Buhler
| editor2   = Peter Stevenhagen
| title     = Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography
| series    = MSRI Publications
| volume    = 44
| publisher = [[Cambridge University Press]]
| year      = 2008
| isbn      = 978-0-521-20833-8
| zbl       = 1154.11002
| url       = https://www.cambridge.org/us/academic/subjects/mathematics/number-theory/algorithmic-number-theory-lattices-number-fields-curves-and-cryptography?format=HB&isbn=9780521808545
}}

* {{서적 인용
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = A Course In Computational Algebraic Number Theory
| year      = 1993
| isbn      = 0-387-55640-0
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 138
| doi = 10.1007/978-3-662-02945-9
}}

* {{서적 인용
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = Advanced Topics in Computational Number Theory
| year      = 2000
| isbn      = 0-387-98727-4
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 193
| doi = 10.1007/978-1-4419-8489-0
}}

* {{서적 인용
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = Number Theory – Volume I: Tools and Diophantine Equations
| year      = 2007
| isbn      = 978-0-387-49922-2
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 239
| doi = 10.1007/978-0-387-49923-9
}}

* {{서적 인용
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = Number Theory – Volume II: Analytic and Modern Tools
| year      = 2007
| isbn      = 978-0-387-49893-5
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 240
| doi = 10.1007/978-0-387-49894-2
}}

* {{서적 인용
| author1   = Richard Crandall | author1-link = Richard Crandall
| author2   = Carl Pomerance | author2-link = Carl Pomerance
| title     = Prime Numbers: A Computational Perspective
| publisher = Springer-Verlag
| year      = 2001
| isbn      = 0-387-94777-9
| doi = 10.1007/978-1-4684-9316-0
}}

* {{서적 인용
| author     = Hans Riesel
| authorlink = Hans Riesel
| title      = Prime Numbers and Computer Methods for Factorization
| edition    = second
| publisher  = Birkhäuser
| year       = 1994
| isbn       = 0-8176-3743-5
| zbl        = 0821.11001
| series     = Progress in Mathematics
| volume     = 126
}}

* {{서적 인용
| author      = Victor Shoup
| author-link = Victor Shoup
| title       = A Computational Introduction to Number Theory and Algebra
| publisher   = [[Cambridge University Press]]
| year        = 2012
| isbn        = 9781139165464
| doi         = 10.1017/CBO9781139165464
}}

* {{서적 인용
| author     = Samuel S. Wagstaff, Jr.
| authorlink = Samuel S. Wagstaff, Jr.
| title      = The Joy of Factoring
| publisher  = American Mathematical Society
| year       = 2013
| isbn       = 978-1-4704-1048-3
| url        = https://www.ams.org/bookpages/stml-68
}}

== 각주 ==
{{각주|refs=

<ref name=pcm>{{인용
| author1    = Carl Pomerance | author1-link = Carl Pomerance
| editor1    = Timothy Gowers | editor1-link = Timothy Gowers
| title      = Computational Number Theory
| work       = The Princeton Companion to Mathematics
| publisher  = [[Princeton University Press]]
| year       = 2009
| url        = https://math.dartmouth.edu/~carlp/PDF/pcm0049.pdf
}}</ref>

<ref name=bachshallit>{{서적 인용
| author1   = Eric Bach | author1-link = Eric Bach
| author2   = Jeffrey Shallit | author2-link = Jeffrey Shallit
| title     = Algorithmic Number Theory, Volume 1: Efficient Algorithms
| publisher = MIT Press
| year      = 1996
| isbn      = 0-262-02405-5
}}</ref>

<ref name=cohen>{{서적 인용
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = A Course In Computational Algebraic Number Theory
| year      = 1993
| isbn      = 0-387-55640-0
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 138
| doi = 10.1007/978-3-662-02945-9
}}</ref>
}}

{{수론 알고리즘}}
{{수론}}

[[분류:계산수론| ]]
[[분류:수론]]
[[분류:계산 학문 분야]]