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Mathematics

D-Index
54
Citations
11664
World Ranking
836
National Ranking
19

Research.com Recognitions

  • 2006 - Fellow of the Australian Academy of Science

Overview

Igor E. Shparlinski is affiliated with the University of New South Wales in Australia. Their research spans the fields of Mathematics and Computer Science, with a substantial focus on Algebra and Number Theory, Discrete Mathematics and Combinatorics, Artificial Intelligence, Geometry and Topology, and Mathematical Physics.

The main topics covered in their work include:

  • Analytic Number Theory Research
  • Coding theory and cryptography
  • Limits and Structures in Graph Theory
  • Algebraic Geometry and Number Theory
  • Finite Group Theory Research
  • Mathematical Dynamics and Fractals
  • Advanced Mathematical Identities

Several recent papers authored or co-authored by Shparlinski highlight their contributions in various specialized areas:

  • "Bilinear forms in Weyl sums for modular square roots and applications" (2020), published in UNSWorks (University of New South Wales, Sydney, Australia)
  • "On large values of Weyl sums" (2020), published in UNSWorks (University of New South Wales, Sydney, Australia)
  • "Congruences with intervals and arbitrary sets" (2020), published in UNSWorks (University of New South Wales, Sydney, Australia)
  • "Hausdorff dimension of the large values of Weyl sums" (2020), published in Journal of Number Theory
  • "On the Structure of Graphs of Markoff Triples" (2020), published in The Quarterly Journal of Mathematics

Frequent co-authors collaborating with Shparlinski include:

  • Alina Ostafe
  • Bryce Kerr
  • Changhao Chen
  • László Mérai
  • Moubariz Z. Garaev

Their publication record encompasses several academic venues where they have consistently contributed, including:

  • arXiv (Cornell University)
  • Journal of Number Theory
  • UNSWorks (University of New South Wales, Sydney, Australia)
  • Finite Fields and Their Applications
  • Canadian Mathematical Bulletin

In terms of book publications, Igor E. Shparlinski has contributed to the American Mathematical Society's volume titled 75 Years of Mathematics of Computation published in 2020.

They have been recognized as a Fellow of the Australian Academy of Science since 2006.

Best Publications

  • Character Sums with Exponential Functions and their Applications

    Sergei Konyagin;Igor Shparlinski

  • The Insecurity of the Digital Signature Algorithm with Partially Known Nonces

    Unknown

  • The insecurity of the digital signature algorithm with partially known nonces

    Phong Q. Nguyen;Igor E. Shparlinski

  • The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces

    Phong Q. Nguyen;Igor E. Shparlinski

  • Finite Fields: Theory and Computation: The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography

    Igor Shparlinski

  • Elliptic divisibility sequences

    Graham Everest;Alf van der Poorten;Igor Shparlinski;Thomas Ward

  • Finite Fields: Theory and Computation

    Igor E. Shparlinski

  • Computational and Algorithmic Problems in Finite Fields

    Igor E. Shparlinski

  • Parameters Of Integral Circulant Graphs And Periodic Quantum Dynamics

    Nitin Saxena;Simone Severini;Igor E. Shparlinski

  • On the statistical properties of Diffie-Hellman distributions

    Ran Canetti;John Friedlander;Sergei Konyagin;Michael Larsen

  • Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness

    Igor E. Shparlinski

  • Period of the power generator and small values of Carmichael's function

    John B. Friedlander;Carl Pomerance;Igor E. Shparlinski

  • Graphs with integral spectrum

    Omran Ahmadi;Noga Alon;Ian F. Blake;Igor E. Shparlinski

  • Cryptographic Applications of Analytic Number Theory

    Igor Shparlinski

  • On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields

    David R. Kohel;Igor Shparlinski

  • Character sums with exponential functions

    John B. Friedlander;Jan Hansen;Igor E. Shparlinski

  • Distribution of Modular Sums and the Security of the Server Aided Exponentiation

    Phong Q. Nguyen;Igor E. Shparlinski;Jacques Stern

  • On Polynomial Approximation of the Discrete Logarithm and the Diffie--Hellman Mapping

    Don Coppersmith;Igor Shparlinski

  • Pseudorandomness and Dynamics of Fermat Quotients

    Alina Ostafe;Igor E. Shparlinski

  • On the cycle structure of repeated exponentiation modulo a prime

    Wun Seng Chou;Igor E. Shparlinski

  • Recent Advances in the Theory of Nonlinear Pseudorandom Number Generators

    Harald Niederreiter;Igor E. Shparlinski

Frequent Co-Authors

John B. Friedlander
John B. Friedlander University of Toronto
Joachim von zur Gathen
Joachim von zur Gathen University of Bonn
Carl Pomerance
Carl Pomerance Dartmouth College
Jean Bourgain
Jean Bourgain Institute for Advanced Study
Harald Niederreiter
Harald Niederreiter Austrian Academy of Sciences
Marek Karpinski
Marek Karpinski University of Bonn
Phong Q. Nguyen
Phong Q. Nguyen French Institute for Research in Computer Science and Automation - INRIA
Umberto Zannier
Umberto Zannier Scuola Normale Superiore di Pisa
Ron Steinfeld
Ron Steinfeld Monash University
Pierre-Alain Fouque
Pierre-Alain Fouque University of Rennes

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