Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
HFE based multi-variate quadratic cryptosystems and Dembowski Ostrom polynomials
Download
index.pdf
Date
2013
Author
Alam, Bilal
Metadata
Show full item record
Item Usage Stats
176
views
87
downloads
Cite This
Harayama and Friesen proposed linearised binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski Ostrom(DO) polynomials in this framework over the finite fi eld F2. They conjecture about the existence of infi nite class of weak DO polynomials and presented the open problem of enumerating their classes. We extend linearised binomial attack to multivariate quadratic cryptosystems over Fp for any prime p and redefi ne the weak DO polynomials for general case. We identify an in finite class of weak Dembowski Ostrom polynomials for these systems by considering highly degenerate quadratic forms over algebraic function fields and Artin-Schreir type curves to achieve our results. This thesis also presents a comprehensive survey of HFE based multivariate quadratic publickey cryptosystems and discusses some recent cryptanalytic attacks involving Grobner bases and matrix/vector operations by reducing the involved problem to related MinRank and IP problem. We also mention a possible connection among Ore's p-polynomials and HFE cryptosystems identifi ed in the work of Coulter.
Subject Keywords
Polynomials.
,
Orthogonal polynomials.
,
Binomial theorem.
,
Cryptography.
URI
http://etd.lib.metu.edu.tr/upload/12616136/index.pdf
https://hdl.handle.net/11511/22837
Collections
Graduate School of Applied Mathematics, Thesis
Suggestions
OpenMETU
Core
Calculations of the roots of classical orthogonal polynomials: an application to gaussian quadrature
Shaidolda, Gulnaz; Taşeli, Hasan; Department of Mathematics (2019)
This thesis focuses on classical orthogonal polynomials namely Jacobi, Laguerre and Hermite polynomials and a method to calculate the roots of these polynomials is constructed. The roots are expressed as the eigenvalues of a tridiagonal matrix whose coefficients depend on the recurrence formula for the classical orthogonal polynomials. These approximations of roots are used as method of computation of Gaussian quadratures. Then the discussion of the numerical results are then introduced to deduce the effici...
Randomness properties of some vector sequences generated by multivariate polynomial iterations
Gürkan Balıkçıoğlu, Pınar; Diker Yücel, Melek; Department of Cryptography (2016)
We examine the randomness properties of the sequences generated by the multivariate polynomial iterations method proposed by Ostafe and Shparlinski, by using the six different choices of polynomials given by the same authors. Our analysis is based on two approaches: distributions of the periods and linear complexities of the produced vector sequences. We define the efficiency parameters, PE for “period efficiency” and LCE for “linear complexity efficiency”, so that the actual values of the period and linear com...
Restricted Modules and Conjectures on Modules of Constant Jordan Type
Öztürk, Semra (Springer, 2014-01-01)
We introduce the class of restricted k[A]-modules and p t-Jordan types for a finite abelian p-group A of exponent at least p t and a field k of characteristic p. For these modules, we generalize several theorems by Benson, verify a generalization of conjectures stated by Suslin and Rickard giving constraints on Jordan types for modules of constant Jordan type when t is 1. We state conjectures giving constraints on p t-Jordan types and show that many p t-Jordan types are realizable.
Polynomial Multiplication over Finite Fields using Field Extensions and Interpolation
Cenk, Murat; Özbudak, Ferruh (2009-06-10)
A method for polynomial multiplication over finite fields using field extensions and polynomial interpolation is introduced. The proposed method uses polynomial interpolation as Toom-Cook method together with field extensions. Furthermore, the proposed method can be used when Toom-Cook method cannot be applied directly. Explicit formulae improving the previous results in many cases are obtained.
Additive polynomials and primitive roots over finite fields
Özbudak, Ferruh (2001-01-01)
We prove existence of primitive roots with a prescribed nonzero image using the arithmetic of algebraic function fields for a class of polynomials over sufficiently large finite fields.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
B. Alam, “HFE based multi-variate quadratic cryptosystems and Dembowski Ostrom polynomials,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.