12 citations · 70 across the 40 of their papers we have counts for
7 papers · 1 filter
On Quadratic Fields Generated by Discriminants of Irreducible Trinomials
I. E. Shparlinski
A. Mukhopadhyay, M. R. Murty and K. Srinivas (http://arxiv.org/abs/0808.0418) have recently studied various arithmetic properties of the discriminant of the trinomial $f…
On the Distribution of the Euler Function of Shifted Smooth Numbers
Stefanie S. Loiperdinger, Igor E. Shparlinski
We give asymptotic formulas for some average values of the Euler function on shifted smooth numbers. The result is based on various estimates on the distribution of smooth numbers…
Divisibility, Smoothness and Cryptographic Applications
David Naccache, Igor E. Shparlinski
This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth numbers play a crucial role in information theory, signal processing and cryptogr…
On the Sum-Product Problem on Elliptic Curves
Omran Ahmadi, Igor Shparlinski
Let $\E$ be an ordinary elliptic curve over a finite field $\F_{q}$ of elements and denote the -coordinate of a point on $\E$. Given an $\F_q$-ratio…
Classical and Quantum Algorithms for Exponential Congruences
Wim van Dam, Igor E. Shparlinski
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum a…
On a Generalised Lehmer Problem for Arbitrary Powers
I. E. Shparlinski
We consider a generalisation of the classical Lehmer problem about the parity distribution of an integer and its modular inverse. We use some known estimates of exponential sums to…