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Algorithms for Abelian Surfaces over Finite Fields and Their Applications to Cryptography.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algorithms for Abelian Surfaces over Finite Fields and Their Applications to Cryptography./
作者:	Chu, Hao-Wei.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	122 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
Contained By:	Dissertations Abstracts International83-03B.
標題:	Cryptography. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28841704
ISBN:	9798460448562

Algorithms for Abelian Surfaces over Finite Fields and Their Applications to Cryptography.
Chu, Hao-Wei.

Algorithms for Abelian Surfaces over Finite Fields and Their Applications to Cryptography. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 122 p.

Source: Dissertations Abstracts International, Volume: 83-03, Section: B.

Thesis (Ph.D.)--The Pennsylvania State University, 2021.

This item must not be sold to any third party vendors.

This dissertation investigates two types of abelian surfaces: superspecial abelian surfaces over finite fields and abelian surfaces over number fields with complex multiplication. We generalize theorems for elliptic curves to these surfaces, and discuss their applications in cryptography.In the first part, by extending Page's algorithm in 2014, we give a probabilistic algorithm that solves principal ideal problems over matrix algebras over quaternion algebras in subexponential time in the size of the ideal and the determinant of the quaternion algebra. We also discuss their applications to cryptography protocols based on isogenies on superspecial abelian surfaces.In the second part, we discuss a p-adic algorithm which computes the Igusa class polynomial of a quartic CM field, which encodes abelian surfaces with complex multiplication by the field. We discuss potential improvements to the canonical lifting algorithm by Carls and Lubicz in 2009, which is the core of the p-adic algorithm. Applying the improvement, we computed examples for p = 5 and 7. We also analyze the computational complexity for the entire p-adic algorithm.

ISBN: 9798460448562Subjects--Topical Terms:

532586
Cryptography.
Subjects--Index Terms:

Cryptography

Algorithms for Abelian Surfaces over Finite Fields and Their Applications to Cryptography.
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100 1 $a Chu, Hao-Wei. $3 3692465
245 1 0 $a Algorithms for Abelian Surfaces over Finite Fields and Their Applications to Cryptography.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 122 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
500 $a Advisor: Eisentraeger, Kirsten.
502 $a Thesis (Ph.D.)--The Pennsylvania State University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a This dissertation investigates two types of abelian surfaces: superspecial abelian surfaces over finite fields and abelian surfaces over number fields with complex multiplication. We generalize theorems for elliptic curves to these surfaces, and discuss their applications in cryptography.In the first part, by extending Page's algorithm in 2014, we give a probabilistic algorithm that solves principal ideal problems over matrix algebras over quaternion algebras in subexponential time in the size of the ideal and the determinant of the quaternion algebra. We also discuss their applications to cryptography protocols based on isogenies on superspecial abelian surfaces.In the second part, we discuss a p-adic algorithm which computes the Igusa class polynomial of a quartic CM field, which encodes abelian surfaces with complex multiplication by the field. We discuss potential improvements to the canonical lifting algorithm by Carls and Lubicz in 2009, which is the core of the p-adic algorithm. Applying the improvement, we computed examples for p = 5 and 7. We also analyze the computational complexity for the entire p-adic algorithm.
590 $a School code: 0176.
650 4 $a Cryptography. $3 532586
650 4 $a Algebra. $3 516203
650 4 $a Polynomials. $3 604754
650 4 $a Algorithms. $3 536374
650 4 $a Mathematics. $3 515831
653 $a Cryptography
690 $a 0405
710 2 $a The Pennsylvania State University. $3 699896
773 0 $t Dissertations Abstracts International $g 83-03B.
790 $a 0176
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28841704