H-Index & Metrics Top Publications
Igor E. Shparlinski

Igor E. Shparlinski

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 46 Citations 8,952 606 World Ranking 730 National Ranking 21

Research.com Recognitions

Awards & Achievements

2006 - Fellow of the Australian Academy of Science

Overview

What is he best known for?

The fields of study he is best known for:

  • Combinatorics
  • Algebra
  • Discrete mathematics

Igor E. Shparlinski mainly investigates Discrete mathematics, Combinatorics, Finite field, Pseudorandom number generator and Modulo. His Discrete mathematics research includes themes of Elliptic curve, Polynomial and Discrete logarithm. His work focuses on many connections between Combinatorics and other disciplines, such as Upper and lower bounds, that overlap with his field of interest in Algorithm.

His Finite field study integrates concerns from other disciplines, such as Multiplicative function, Multiplicative order, Element and Primitive element theorem. Igor E. Shparlinski has researched Pseudorandom number generator in several fields, including Linear congruential generator, Inversive and Distribution. His work in Modulo addresses subjects such as Character sum, which are connected to disciplines such as Congruence relation.

His most cited work include:

  • The insecurity of the digital signature algorithm with partially known nonces (173 citations)
  • Character Sums with Exponential Functions and their Applications (167 citations)
  • The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces (134 citations)

What are the main themes of his work throughout his whole career to date?

Igor E. Shparlinski spends much of his time researching Combinatorics, Discrete mathematics, Finite field, Prime and Modulo. He works mostly in the field of Combinatorics, limiting it down to concerns involving Exponential function and, occasionally, Number theory. His research in Discrete mathematics intersects with topics in Pseudorandom number generator, Asymptotic formula, Distribution, Function and Polynomial.

His work carried out in the field of Finite field brings together such families of science as Degree and Elliptic curve, Pure mathematics, Rational function. His study brings together the fields of Sequence and Prime. His study in Modulo is interdisciplinary in nature, drawing from both Riemann hypothesis and Congruence relation.

He most often published in these fields:

  • Combinatorics (50.05%)
  • Discrete mathematics (42.66%)
  • Finite field (28.97%)

What were the highlights of his more recent work (between 2016-2021)?

  • Combinatorics (50.05%)
  • Pure mathematics (16.58%)
  • Finite field (28.97%)

In recent papers he was focusing on the following fields of study:

His primary areas of investigation include Combinatorics, Pure mathematics, Finite field, Prime and Modulo. Combinatorics is closely attributed to Upper and lower bounds in his work. His Pure mathematics research incorporates themes from Multiplicative function, Series and Distribution.

Igor E. Shparlinski has included themes like Quadratic equation and Sequence in his Finite field study. Igor E. Shparlinski interconnects Discrete mathematics, Prime number, Integer sequence and Exponential function in the investigation of issues within Prime. Igor E. Shparlinski applies his multidisciplinary studies on Discrete mathematics and Root of unity in his research.

Between 2016 and 2021, his most popular works were:

  • Prescribing the binary digits of squarefree numbers and quadratic residues (16 citations)
  • Divisor problem in arithmetic progressions modulo a prime power (15 citations)
  • New bounds of Weyl sums (14 citations)

In his most recent research, the most cited papers focused on:

  • Combinatorics
  • Algebra
  • Real number

The scientist’s investigation covers issues in Combinatorics, Pure mathematics, Finite field, Prime and Upper and lower bounds. His Combinatorics research is multidisciplinary, relying on both Arithmetic function and Sequence. His Pure mathematics research integrates issues from Multiplicative function, Algebraic number and Distribution.

His research integrates issues of Graph, Multiplicative order, Polynomial interpolation, Partition and Connected component in his study of Finite field. His work deals with themes such as Discrete mathematics, Quadratic residue, Square-free integer, Quadratic equation and Exponential function, which intersect with Prime. In his articles, Igor E. Shparlinski combines various disciplines, including Discrete mathematics and Quantum algorithm.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

Character Sums with Exponential Functions and their Applications

Sergei Konyagin;Igor Shparlinski.
(1999)

278 Citations

The insecurity of the digital signature algorithm with partially known nonces

Phong Q. Nguyen;Igor E. Shparlinski.
Journal of Cryptology (2002)

248 Citations

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

Phong Q. Nguyen;Igor E. Shparlinski.
Designs, Codes and Cryptography (2003)

198 Citations

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

Igor Shparlinski.
(1999)

166 Citations

Elliptic divisibility sequences

Graham Everest;Alf van der Poorten;Igor Shparlinski;Thomas Ward.
(2003)

131 Citations

Finite Fields: Theory and Computation

Igor E. Shparlinski.
(1999)

119 Citations

Computational and Algorithmic Problems in Finite Fields

Igor E. Shparlinski.
(1992)

113 Citations

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

Igor E. Shparlinski.
(2002)

112 Citations

On the statistical properties of Diffie-Hellman distributions

Ran Canetti;John Friedlander;Sergei Konyagin;Michael Larsen.
Israel Journal of Mathematics (2000)

111 Citations

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

John B. Friedlander;Carl Pomerance;Igor E. Shparlinski.
Mathematics of Computation (2001)

105 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

If you think any of the details on this page are incorrect, let us know.

Contact us

Top Scientists Citing Igor E. Shparlinski

Harald Niederreiter

Harald Niederreiter

Austrian Academy of Sciences

Publications: 26

Carl Pomerance

Carl Pomerance

Dartmouth College

Publications: 22

Joseph H. Silverman

Joseph H. Silverman

Brown University

Publications: 20

Tanja Lange

Tanja Lange

Eindhoven University of Technology

Publications: 19

Jean Bourgain

Jean Bourgain

Institute for Advanced Study

Publications: 18

Pierre-Alain Fouque

Pierre-Alain Fouque

University of Rennes 1

Publications: 15

Ivan Gutman

Ivan Gutman

University of Kragujevac

Publications: 12

Xiang-Gen Xia

Xiang-Gen Xia

University of Delaware

Publications: 11

Eike Kiltz

Eike Kiltz

Ruhr University Bochum

Publications: 9

Daniel J. Bernstein

Daniel J. Bernstein

University of Illinois at Chicago

Publications: 9

Michael N. Vrahatis

Michael N. Vrahatis

University of Patras

Publications: 9

Xiaofeng Chen

Xiaofeng Chen

Xidian University

Publications: 8

Chris Godsil

Chris Godsil

University of Waterloo

Publications: 8

Alfred Menezes

Alfred Menezes

University of Waterloo

Publications: 7

Jin Li

Jin Li

Guangzhou University

Publications: 7

Something went wrong. Please try again later.