Index Generation Functions Based on Linear and Polynomial Transformations

2016 ◽  
Author(s):  
Helena Astola ◽  
Radomir S. Stankovic ◽  
Jaakko T. Astola
Keyword(s):  
Polynomial Transformations

Transitive polynomial transformations of residue class rings

2002 ◽  
Vol 12 (2) ◽  
Author(s):  
M.V. Larin
Keyword(s):  
Residue Class ◽  
Integer Coefficients ◽  
Polynomial Transformations

AbstractWe give a complete description of the polynomials f(x) with integer coefficients such that the period of the recurring sequence u

Application of formal languages in polynomial transformations of instances between NP-complete problems

2013 ◽  
Vol 14 (8) ◽  
pp. 623-633
Author(s):  
Jorge A. Ruiz-Vanoye ◽  
Joaquín Pérez-Ortega ◽  
Rodolfo A. Pazos Rangel ◽  
Ocotlán Díaz-Parra ◽  
Héctor J. Fraire-Huacuja ◽  
...  
Keyword(s):  
Formal Languages ◽  
Complete Problems ◽  
Polynomial Transformations ◽  
Np Complete

scholarly journals Survey of polynomial transformations between NP-complete problems

2011 ◽  
Vol 235 (16) ◽  
pp. 4851-4865 ◽  
Author(s):  
Jorge A. Ruiz-Vanoye ◽  
Joaquín Pérez-Ortega ◽  
Rodolfo A. Pazos R. ◽  
Ocotlán Díaz-Parra ◽  
Juan Frausto-Solís ◽  
...  
Keyword(s):  
Complete Problems ◽  
Polynomial Transformations ◽  
Np Complete

Explicit constructions of extremal graphs and new multivariate cryptosystems

2015 ◽  
Vol 52 (2) ◽  
pp. 185-204 ◽  
Author(s):  
Vasyl Ustimenko
Keyword(s):  
Discrete Logarithm ◽  
Public Key Infrastructure ◽  
Public Key ◽  
Polynomial Degree ◽  
Affine Spaces ◽  
Private Key ◽  
Explicit Constructions ◽  
Diffie Hellman ◽  
Polynomial Transformations ◽  
Finite Commutative Ring

New multivariate cryptosystems are introduced. Sequences f(n) of bijective polynomial transformations of bijective multivariate transformations of affine spaces Kn, n = 2, 3, ... , where K is a finite commutative ring with special properties, are used for the constructions of cryptosystems. On axiomatic level, the concept of a family of multivariate maps with invertible decomposition is proposed. Such decomposition is used as private key in a public key infrastructure. Requirements of polynomiality of degree and density allow to estimate the complexity of encryption procedure for a public user. The concepts of stable family and family of increasing order are motivated by studies of discrete logarithm problem in Cremona group. Statement on the existence of families of multivariate maps of polynomial degree and polynomial density with the invertible decomposition is formulated. We observe known explicit constructions of special families of multivariate maps. They correspond to explicit constructions of families of nonlinear algebraic graphs of increasing girth which appeared in Extremal Graph Theory. The families are generated by pseudorandom walks on graphs. This fact ensures the existence of invertible decomposition; a certain girth property guarantees the increase of order for the family of multivariate maps, good expansion properties of families of graphs lead to good mixing properties of graph based private key algorithms. We describe the general schemes of cryptographic applications of such families (public key infrastructure, symbolic Diffie—Hellman protocol, functional versions of El Gamal algorithm).

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