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.

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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