A nonlinear elliptic curve cryptosystem based on matrices

被引：11

作者：

Climent, JJ ^{[1
]}

Ferrández, F ^{[1
]}

Vicent, JF ^{[1
]}

Zamora, A ^{[1
]}

机构：

[1] Univ Alacant, Dept Ciencia Computac & Intelligencia Artificial, E-03080 Alacant, Spain

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 174卷 / 01期

关键词：

public key cryptography; elliptic curves; discrete logarithm problem; elliptic curve discrete logarithm problem; finite field; Diffie-Hellman key agreement;

D O I：

10.1016/j.amc.2005.03.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a new mathematical problem that is applicable to public key cryptography. Based on the Discrete Logarithm Problem (DLP), it uses certain elements formed by two matrices with elements in a finite field and a matrix whose elements are points of an elliptic curve. With this system, we get a larger key space without increasing the underlying elliptic curve and, consequently, without the computational requirements inherent to the set up of elliptic Curves at random. Also, we expose the Diffie-Hellman key agreement protocol with this system acting as the underlying mathematical problem. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：150 / 164

页数：15

共 50 条

[21] Digital signature scheme resulted from identification protocol by elliptic curve cryptosystem
Chen, TS
Huang, GS
Liu, TP
Chung, YF
2002 IEEE REGION 10 CONFERENCE ON COMPUTERS, COMMUNICATIONS, CONTROL AND POWER ENGINEERING, VOLS I-III, PROCEEDINGS, 2002, : 192 - 195
[22] A New Modified Cryptosystem Based on Menezes Vanstone Elliptic Curve Cryptography Algorithm that Uses Characters' Hexadecimal Values
Kurt, Meltem
Yerlikaya, Tarik
2013 INTERNATIONAL CONFERENCE ON TECHNOLOGICAL ADVANCES IN ELECTRICAL, ELECTRONICS AND COMPUTER ENGINEERING (TAEECE), 2013, : 449 - 453
[23] A Non-Reducible Meyer-Muller's Like Elliptic Curve Cryptosystem
Martinez, S.
Miret, J. M.
Sebe, F.
Tomas, R.
IEEE LATIN AMERICA TRANSACTIONS, 2012, 10 (03) : 1730 - 1733
[24] Expander graphs based on GRH with an application to elliptic curve cryptography
Jao, David
Miller, Stephen D.
Venkatesan, Ramarathnam
JOURNAL OF NUMBER THEORY, 2009, 129 (06) : 1491 - 1504
[25] A Low-Cost and High-Performance Cryptosystem Using Tripling-Oriented Elliptic Curve
Alkhatib, Mohammad
Aldalbahy, Wafa S.
INTELLIGENT AUTOMATION AND SOFT COMPUTING, 2023, 37 (02) : 1807 - 1831
[26] Elliptic Curves Cryptosystem Based Electronic Cash Scheme with Parameter Optimization
Zhou, Xuanwu
2009 PACIFIC-ASIA CONFERENCE ON KNOWLEDGE ENGINEERING AND SOFTWARE ENGINEERING, PROCEEDINGS, 2009, : 182 - 185
[27] The state of elliptic curve cryptography
Koblitz, N
Menezes, A
Vanstone, S
DESIGNS CODES AND CRYPTOGRAPHY, 2000, 19 (2-3) : 173 - 193
[28] The State of Elliptic Curve Cryptography
Neal Koblitz
Alfred Menezes
Scott Vanstone
Designs, Codes and Cryptography, 2000, 19 : 173 - 193
[29] Elliptic curve Paillier schemes
Galbraith, SD
JOURNAL OF CRYPTOLOGY, 2002, 15 (02) : 129 - 138
[30] A new ElGamal-like cryptosystem based on matrices over groupring
Saba Inam
Rashid Ali
Neural Computing and Applications, 2018, 29 : 1279 - 1283

← 1 2 3 4 5 →