2006 - Fellow of the Australian Academy of Science
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.
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.
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.
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.
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Character Sums with Exponential Functions and their Applications
Sergei Konyagin;Igor Shparlinski.
(2010)
The insecurity of the digital signature algorithm with partially known nonces
Phong Q. Nguyen;Igor E. Shparlinski.
Journal of Cryptology (2002)
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
Phong Q. Nguyen;Igor E. Shparlinski.
Designs, Codes and Cryptography (2003)
Finite Fields: Theory and Computation: The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography
Igor Shparlinski.
(1999)
Elliptic divisibility sequences
Graham Everest;Alf van der Poorten;Igor Shparlinski;Thomas Ward.
(2003)
Computational and Algorithmic Problems in Finite Fields
Igor E. Shparlinski.
(1992)
Finite Fields: Theory and Computation
Igor E. Shparlinski.
(1999)
On the statistical properties of Diffie-Hellman distributions
Ran Canetti;John Friedlander;Sergei Konyagin;Michael Larsen.
Israel Journal of Mathematics (2000)
Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness
Igor E. Shparlinski.
(2002)
Period of the power generator and small values of Carmichael's function
John B. Friedlander;Carl Pomerance;Igor E. Shparlinski.
Mathematics of Computation (2001)
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