scholarly journals Dihedral Group Codes over Finite Fields

Author(s):  
Yun Fan ◽  
Liren Lin
Author(s):  
Adnan A. Zain

For group codes over elementary Abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group. We also lift the theorem that relates the parity check and the generator matrices of linear codes over finite fields to group codes over elementary Abelian groups. Some new codes that are MDS, self-dual, and cyclic over the Abelian group with four elements are given.


2020 ◽  
Vol 24 (9) ◽  
pp. 1894-1898
Author(s):  
Yanyan Gao ◽  
Qin Yue ◽  
Xinmei Huang

Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  

2018 ◽  
Vol 43 (1-4) ◽  
pp. 13-45
Author(s):  
Prof. P. L. Sharma ◽  
◽  
Mr. Arun Kumar ◽  
Mrs. Shalini Gupta ◽  
◽  
...  

2020 ◽  
Vol 25 (4) ◽  
pp. 4-9
Author(s):  
Yerzhan R. Baissalov ◽  
Ulan Dauyl

The article discusses primitive, linear three-pass protocols, as well as three-pass protocols on associative structures. The linear three-pass protocols over finite fields and the three-pass protocols based on matrix algebras are shown to be cryptographically weak.


Vestnik MEI ◽  
2018 ◽  
Vol 5 (5) ◽  
pp. 79-88
Author(s):  
Sergey B. Gashkov ◽  
◽  
Aleksandr B. Frolov ◽  
Elizaveta Р. Popova ◽  
◽  
...  

Author(s):  
Anna ILYENKO ◽  
Sergii ILYENKO ◽  
Yana MASUR

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.


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