NDLI: Further refinements of Miller’s algorithm on Edwards curves

Please wait, while we are loading the content...

Further refinements of Miller’s algorithm on Edwards curves

Content Provider	Springer Nature Link
Author	Le, Duc Phong Tan, Chik How
Copyright Year	2015
Abstract	Recently, Edwards curves have received a lot of attention in the cryptographic community due to their fast scalar multiplication algorithms. Then, many works on the application of these curves to pairing-based cryptography have been introduced. In this paper, we investigate refinements to Miller’s algorithm that play a central role in paring computation. We first introduce a variant of Miller function that leads to a more efficient variant of Miller’s algorithm on Edwards curves. Then, based on the new Miller function, we present a refinement to Miller’s algorithm that significantly improves the performance in comparison with the original Miller’s algorithm. Our analyses also show that the proposed refinement is approximately 25 % faster than Xu–Lin’s refinements (CT-RSA, 2010). Last but not least, our approach is generic, hence the proposed algorithms allow to compute both Weil and Tate pairings on pairing-friendly Edwards curves of any embedding degree.
Ending Page	217
Page Count	13
Starting Page	205
File Format	PDF
ISSN	09381279
e-ISSN	14320622
Journal	Applicable Algebra in Engineering, Communication and Computing
Issue Number	3
Volume Number	27
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-11-04
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Miller’s algorithm Computer Hardware Artificial Intelligence (incl. Robotics) Pairing computation Edwards curves Algebraic coding theory; cryptography Theory of Computation Tate/Weil pairings Symbolic and Algebraic Manipulation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Multibase scalar multiplications in cryptographic pairings

Improved Miller’s Algorithm for Computing Pairings on Edwards Curves

A simple method for obtaining relations among factor basis elements for special hyperelliptic curves

Polynomial interpolation of the Naor–Reingold pseudo-random function

Predicting the elliptic curve congruential generator

New algorithm for the elliptic curve discrete logarithm problem with auxiliary inputs

Improved Weil and Tate pairings for elliptic and hyperelliptic curves

Computational hardness of IFP and ECDLP

FURTHER REFINEMENT OF PAIRING COMPUTATION BASED ON MILLER’S ALGORITHM

Further refinements of Miller’s algorithm on Edwards curves

Similar Documents

Multibase scalar multiplications in cryptographic pairings

Improved Miller’s Algorithm for Computing Pairings on Edwards Curves

A simple method for obtaining relations among factor basis elements for special hyperelliptic curves

Polynomial interpolation of the Naor–Reingold pseudo-random function

Predicting the elliptic curve congruential generator

New algorithm for the elliptic curve discrete logarithm problem with auxiliary inputs

Improved Weil and Tate pairings for elliptic and hyperelliptic curves

Computational hardness of IFP and ECDLP

FURTHER REFINEMENT OF PAIRING COMPUTATION BASED ON MILLER’S ALGORITHM

Further refinements of Miller’s algorithm on Edwards curves