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**Date:** 2011
**Subject Keyword:**
010100 Pure Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/163352
**Description:**
We estimate the number of possible degree patterns of k-lacunary polynomials of degree t<p which split completely modulo p. The result is based on a combination of a bound on the number of zeros of la
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**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2006
**Subject Keyword:**
010100 Pure Mathematics
| 010200 Applied Mathematics
| 010500 Mathematical Physics
| distance problems
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/20160
**Description:**
We use bounds of exponential sums to derive new lower bounds on the number of distinct distances between all pairs of points (x,y) ∈ A×B for two given sets A,B ∈ Fnq, where Fq is a finite field of q e
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**Full Text:**
**Reviewed:**
**Date:** 2008
**Subject Keyword:**
010100 Pure Mathematics
| 080200 Computation Theory and Mathematics
| 080400 Data Format
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1244068
**Description:**
7 page(s)
**Reviewed:**
**Date:** 2008
**Subject Keyword:**
010100 Pure Mathematics
| 080200 Computation Theory and Mathematics
| energy of graphs
| circulant graphs
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/81856
**Description:**
We obtain upper and lower bounds on the average energy of circulant graphs with n vertices and regularity d. The average is taken over all representations of such graphs by circulant adjacency matrice
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**Reviewed:**
**Date:** 2009
**Subject Keyword:**
080200 Computation Theory and Mathematics
| elliptic curve cryptography
| hashing
| Chebotarev density theorem
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/145345
**Description:**
We study the hash function from a finite field Fq into an elliptic curve over Fq which has recently been introduced by T. Icart. In particular we slightly adjust and prove the asymptotic formula conje
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**Full Text:**
**Reviewed:**
**Authors:**
Farashahi, Reza R
| Fouque, Pierre-Alain
| Shparlinski, Igor E
| Tibouchi, Mehdi
| Voloch, J. Felipe
**Date:** 2013
**Subject Keyword:**
080200 Computation Theory and Mathematics
| Elliptic curve cryptography
| Exponential sums
| Hashing
| Pseudorandomness
| Random oracle model
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/221564
**Description:**
At Crypto 2010, Brier et al. proposed the first construction of a hash function into ordinary elliptic curves that was indifferentiable from a random oracle, based on Icart's deterministic encoding fr
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**Reviewed:**
**Date:** 2006
**Subject Keyword:**
010200 Applied Mathematics
| 010300 Numerical and Computational Mathematics
| 080200 Computation Theory and Mathematics
| Euler function
| integer factorisation
| NP-completeness
| prime k-tuplet conjecture
| partition problem
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/43466
**Description:**
Given an integer n, how hard is it to find the set of all integers m such that φ(m) = n, where φ is the Euler totient function? We present a certain basic algorithm which, given the prime number facto
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**Full Text:**
**Reviewed:**
**Authors:**
Camburu, Oana-Maria
| Ciolan, Emil-Alexandru
| Luca, Florian
| Moree, Pieter
| Shparlinski, Igor E
**Date:** 2016
**Subject Keyword:**
coefficients of cyclotomic polynomials
| products of primes
| numerical semigroups
| double Kloosterman sums
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1195102
**Description:**
We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduc
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**Reviewed:**
**Date:** 2016
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1195121
**Description:**
There is a well-known asymptotic formula, due to W. M. Schmidt [Duke Math. J., 35 (1968), pp. 327-339], for the number of full-rank integer lattices of index at most V in ℤⁿ. This set of lattices L ca
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**Reviewed:**
**Date:** 2006
**Subject Keyword:**
080200 Computation Theory and Mathematics
| elliptic curves
| pairing
| embedding degree
| MNT curves
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/9947
**Description:**
Miyaji, Nakabayashi and Takano have recently suggested a construction of the so-called MNT elliptic curves with low embedding degree, which are also of importance for pairing-based cryptography. We gi
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**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2012
**Subject Keyword:**
010100 Pure Mathematics
| character sums
| congruences
| exponential sums
| modular hyperbola
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/202794
**Description:**
We give a survey of a variety of recent results about the distribution and some geometric properties of points (x, y) on modular hyperbolas xy ≡ a (mod m). We also outline a very diverse range of appl
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**Reviewed:**
**Date:** 2008
**Subject Keyword:**
010100 Pure Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/81867
**Description:**
In this paper we give upper and lower bounds as well as a heuristic estimate on the number of vertices of the convex closure of the set Gn = {(a, b) : a, b ∈ ℤ, ab ≡ 1 (mod n) , 1 ≤ a, b ≤ n - 1} . Th
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**Reviewed:**
**Date:** 2014
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/332383
**Description:**
We give an upper bound for the number of elliptic Carmichael numbers η ≤ χ that were recently introduced by J. H. Silverman in the case of an elliptic curve without complex multiplication (non CM). We
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**Reviewed:**
**Date:** 2011
**Subject Keyword:**
010100 Pure Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/146331
**Description:**
11 page(s)
**Reviewed:**
**Authors:**
Gathen, par Joachim von zur
| Knopfmacher, Arnold
| Luca, Florian
| Luchtet, Lutz.G
| Shparlinski, Igor E
**Date:** 2004
**Subject Keyword:**
010100 Pure Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1171068
**Description:**
17 page(s)
**Reviewed:**

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