Cover Image

On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions

The extended Euclidean Algorithm is a practical technique used in many cryptographic applications, where it computes the sequences ri, si, ti ∈ ℤ that always satisfy ri = si a+ tib. The integer ri is the remainder in the ith sequences. The sequences si and ti arising from the extended Euclidean algo...

Full description

Saved in:
Bibliographic Details
Main Authors: Muhammad, Khairun Nisak, Kamarulhaili, Hailiza
Format: Conference or Workshop Item
Language:English
Published: AIP Publishing 2016
Online Access:http://psasir.upm.edu.my/id/eprint/57195/1/On%20the%20sequences%20ri%2C%20si%2C%20ti%20%E2%88%88%20%E2%84%A4%20related%20to%20extended%20Euclidean%20algorithm%20and%20continued%20fractions.pdf
http://psasir.upm.edu.my/id/eprint/57195/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.upm.eprints.57195
record_format eprints
spelling my.upm.eprints.571952017-09-08T10:29:58Z http://psasir.upm.edu.my/id/eprint/57195/ On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions Muhammad, Khairun Nisak Kamarulhaili, Hailiza The extended Euclidean Algorithm is a practical technique used in many cryptographic applications, where it computes the sequences ri, si, ti ∈ ℤ that always satisfy ri = si a+ tib. The integer ri is the remainder in the ith sequences. The sequences si and ti arising from the extended Euclidean algorithm are equal, up to sign, to the convergents of the continued fraction expansion of a/b. The values of (ri, si, ti) satisfy various properties which are used to solve the shortest vector problem in representing point multiplications in elliptic curves cryptography, namely the GLV (Gallant, Lambert & Vanstone) integer decomposition method and the ISD (integer sub decomposition) method. This paper is to extend the proof for each of the existing properties on (ri, si, ti). We also generate new properties which are relevant to the sequences ri, si, ti ∈ ℤ. The concepts of Euclidean algorithm, extended Euclidean algorithm and continued fractions are intertwined and the properties related to these concepts are proved. These properties together with the existing properties of the sequence (ri, si, ti) are regarded as part and parcel of the building blocks of a new generation of an efficient cryptographic protocol. AIP Publishing 2016 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57195/1/On%20the%20sequences%20ri%2C%20si%2C%20ti%20%E2%88%88%20%E2%84%A4%20related%20to%20extended%20Euclidean%20algorithm%20and%20continued%20fractions.pdf Muhammad, Khairun Nisak and Kamarulhaili, Hailiza (2016) On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions. In: 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016), 26-28 Jan. 2016, Kuala Lumpur, Malaysia. (pp. 1-8). 10.1063/1.4952482
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description The extended Euclidean Algorithm is a practical technique used in many cryptographic applications, where it computes the sequences ri, si, ti ∈ ℤ that always satisfy ri = si a+ tib. The integer ri is the remainder in the ith sequences. The sequences si and ti arising from the extended Euclidean algorithm are equal, up to sign, to the convergents of the continued fraction expansion of a/b. The values of (ri, si, ti) satisfy various properties which are used to solve the shortest vector problem in representing point multiplications in elliptic curves cryptography, namely the GLV (Gallant, Lambert & Vanstone) integer decomposition method and the ISD (integer sub decomposition) method. This paper is to extend the proof for each of the existing properties on (ri, si, ti). We also generate new properties which are relevant to the sequences ri, si, ti ∈ ℤ. The concepts of Euclidean algorithm, extended Euclidean algorithm and continued fractions are intertwined and the properties related to these concepts are proved. These properties together with the existing properties of the sequence (ri, si, ti) are regarded as part and parcel of the building blocks of a new generation of an efficient cryptographic protocol.
format Conference or Workshop Item
author Muhammad, Khairun Nisak
Kamarulhaili, Hailiza
spellingShingle Muhammad, Khairun Nisak
Kamarulhaili, Hailiza
On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions
author_facet Muhammad, Khairun Nisak
Kamarulhaili, Hailiza
author_sort Muhammad, Khairun Nisak
title On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions
title_short On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions
title_full On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions
title_fullStr On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions
title_full_unstemmed On the sequences ri, si, ti ∈ ℤ related to extended Euclidean algorithm and continued fractions
title_sort on the sequences ri, si, ti ∈ ℤ related to extended euclidean algorithm and continued fractions
publisher AIP Publishing
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/57195/1/On%20the%20sequences%20ri%2C%20si%2C%20ti%20%E2%88%88%20%E2%84%A4%20related%20to%20extended%20Euclidean%20algorithm%20and%20continued%20fractions.pdf
http://psasir.upm.edu.my/id/eprint/57195/
_version_ 1643836414184390656
score 13.211869

Similar Items