Computational Complexity of Checking Identities in 0-Simple Semigroups and Matrix Semigroups over Finite Fields

2006 ◽  
Vol 72 (2) ◽  
pp. 207-222 ◽  
Author(s):  
Steve Seif ◽  
Csaba Szabo
Keyword(s):  
Computational Complexity ◽  
Finite Fields ◽  
Checking Identities ◽  
Matrix Semigroups

Computational Complexity over Finite Fields

1976 ◽  
Vol 5 (2) ◽  
pp. 324-331 ◽  
Author(s):  
Volker Strassen
Keyword(s):  
Computational Complexity ◽  
Finite Fields

scholarly journals On the Families of Stable Multivariate Transformations of Large Order and Their Cryptographical Applications

2017 ◽  
Vol 70 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Vasyl Ustimenko
Keyword(s):  
Computational Complexity ◽  
Commutative Ring ◽  
Finite Fields ◽  
Transformation Groups ◽  
Affine Spaces ◽  
Exponential Order ◽  
Cyclic Groups ◽  
Key Exchange Protocols ◽  
Polynomial Transformations ◽  
High Degree

Abstract Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of with n increasing order can be used in the key exchange protocols and El Gamal multivariate cryptosystems related to them. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via conjugations of two polynomials of kind gk and g−1 given by key holder (Alice) or giving them as elements of different transformation groups. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity.

scholarly journals THE COMPLEXITY OF CHECKING IDENTITIES OVER FINITE GROUPS

2006 ◽  
Vol 16 (05) ◽  
pp. 931-939 ◽  
Author(s):  
GÁBOR HORVÁTH ◽  
CSABA SZABÓ
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Finite Groups ◽  
Abelian Groups ◽  
Single Equation ◽  
Element Group ◽  
Checking Identities

We analyze the computational complexity of solving a single equation and checking identities over finite meta-abelian groups. Among others we answer a question of Goldmann and Russel from 1998: we prove that it is decidable in polynomial time whether or not an equation over the six-element group S3 has a solution.

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields

Maximum Distance Separable Hankel Rhotrices over Finite Fields

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