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- Igor E. Shparlinski

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
46
Citations
9,450
799
World Ranking
970
National Ranking
25

2006 - Fellow of the Australian Academy of Science

- 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.

- 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)

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.

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

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

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.

- 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)

- 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.

Character Sums with Exponential Functions and their Applications

Sergei Konyagin;Igor Shparlinski.

**(2010)**

283 Citations

The insecurity of the digital signature algorithm with partially known nonces

Phong Q. Nguyen;Igor E. Shparlinski.

Journal of Cryptology **(2002)**

260 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)**

218 Citations

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

Igor Shparlinski.

**(1999)**

168 Citations

Elliptic divisibility sequences

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

**(2003)**

140 Citations

Computational and Algorithmic Problems in Finite Fields

Igor E. Shparlinski.

**(1992)**

117 Citations

Finite Fields: Theory and Computation

Igor E. Shparlinski.

**(1999)**

115 Citations

On the statistical properties of Diffie-Hellman distributions

Ran Canetti;John Friedlander;Sergei Konyagin;Michael Larsen.

Israel Journal of Mathematics **(2000)**

113 Citations

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

Igor E. Shparlinski.

**(2002)**

112 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)**

107 Citations

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