The "Elliptic" Matrices and a New Kind of Cryptography

被引：2
作者：
Cheddour, Zakariae [1 ]
Chillali, Abdelhakim [1 ]
Mouhib, Ali [1 ]
机构：
[1] Univ Sidi Mohamed Ben Abdellah USMBA, Dept Math, FP Taza, LSI Lab, Taza, Morocco
来源：
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2023年 / 41卷
关键词：
Cryptosystem; elliptic curves; fully homomorphic encryption; matrices; discrete logarithm problem;
D O I：
10.5269/bspm.62377
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In their article titled "Cryptography Based on the Matrices", A. Chillali et al. introduce a new cryptographic method based on matrices over a finite field F-pn, where p is a prime number. In this paper, we will generate this method in a new group of square block matrices based on an elliptic curve, called "elliptic" matrices.
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页数：12
相关论文
共 17 条
  • [1] Avanzi R., 2006, Handbook of elliptic and hyperelliptic curve cryptography
  • [2] Blake I., 2005, ADV ELLIPTIC CURVE C
  • [3] Blake I.F., 1999, ELLIPTIC CURVES CRYP
  • [4] Boyd C., 2003, Information Security and Cryptography Series
  • [5] Chillali A., 2011, World Acad. of Sci. Eng. & Technol., V78, P848
  • [6] Key exchange protocols over noncommutative rings. The case of End(Zp x Zp2)
    Climent, Joan-Josep
    Navarro, Pedro R.
    Tortosa, Leandro
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2012, 89 (13-14) : 1753 - 1763
  • [7] Cryptanalysis of Some Protocols Using Matrices over Group Rings
    Eftekhari, Mohammad
    [J]. PROGRESS IN CRYPTOLOGY - AFRICACRYPT 2017, 2017, 10239 : 223 - 229
  • [8] A Diffie-Hellman key exchange protocol using matrices over noncommutative rings
    Eftekhari, Mohammad
    [J]. GROUPS COMPLEXITY CRYPTOLOGY, 2012, 4 (01) : 167 - 176
  • [9] Galbraith SD, 2012, MATHEMATICS OF PUBLIC KEY CRYPTOGRAPHY, P1, DOI 10.1017/CBO9781139012843
  • [10] Hankerson D., 2004, Springer professional computing)
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