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**Authors:**
Shparlinski, Igor E
**Date:** 2015
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1197906
**Description:**
We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves E over a prime finite field Fp of p elements, such that the discriminant D(E) o
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**Reviewed:**
**Date:** 2015
**Subject Keyword:**
polynomial congruences
| finite fields
| value sets of polynomials
| multiplicative subgroups
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1195893
**Description:**
13 page(s)
**Reviewed:**
**Date:** 2014
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1194946
**Description:**
Recently, several bounds have been obtained on the number of solutions of congruences of the type (x1+s)⋯(xv+s)≡(y1+s)⋯(yv+s)≢0 (mod p), where p is prime and variables take values in some short inter
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**Reviewed:**
**Date:** 2014
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/324810
**Description:**
We study polynomials with integer coefficients which become Eisenstein polynomials after the additive shift of a variable. We call such polynomials shifted Eisenstein polynomials. We determine an uppe
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**Reviewed:**
**Date:** 2014
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1197832
**Description:**
13 page(s)
**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2014
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/1197920
**Description:**
10 page(s)
**Reviewed:**
**Date:** 2013
**Subject Keyword:**
010100 Pure Mathematics
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/272190
**Description:**
We obtain upper bounds on the number of solutions to congruences of the type (x1 + s)... (xv + s) ≡ (y1 + s)... (xv + s) ≢ 0 (mod p) modulo a prime p with variables from some short intervals. We give
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**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2013
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/271249
**Description:**
We show that for any integers a and m with m ≥ 1 and gcd(a,m) = 1, there is a solution to the congruence pr ≡ a (modm) where p is prime, r is a product of at most k = 17 prime factors and p, r ≤ m. Th
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**Reviewed:**
**Date:** 2013
**Subject Keyword:**
080200 Computation Theory and Mathematics
| Arithmetic functions
| Eisenstein criterion
| Irreducible polynomial
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/231936
**Description:**
We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree d and of height at most H, as H → ∞. In particular, we give an e
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**Reviewed:**
**Date:** 2013
**Subject Keyword:**
080200 Computation Theory and Mathematics
| Cryptography
| Finite fields
| Pseudorandom numbers
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/221905
**Description:**
We study the security of the linear generator over a finite field. It is shown that the seed of a linear generator can be deduced from partial information of a short sequence of consecutive outputs of
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**Reviewed:**
**Date:** 2012
**Subject Keyword:**
010100 Pure Mathematics
| Additive combinatorics
| Orbits
| Polynomial congruences
| Vinogradov mean value theorem
| Visible points
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/205033
**Description:**
For a polynomial f∈Fp[X] , we obtain upper bounds on the number of points (x, f (x)) modulo a prime p which belong to an arbitrary square with the side length H. Our results in particular are based on
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**Reviewed:**
**Authors:**
Shparlinski, Igor E
**Date:** 2012
**Subject Keyword:**
010100 Pure Mathematics
| Distribution of points
| Multivariate congruences
| Polynomials
| Well-shaped domains
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/198238
**Description:**
We use a result of É. Fouvry about the distribution of solutions to systems of congruences with multivariate polynomials in small cubic boxes and some ideas of W. Schmidt to derive an asymptotic formu
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**Reviewed:**
**Date:** 2010
**Subject Keyword:**
080200 Computation Theory and Mathematics
| elliptic curve
| Edwards curve
| j-Invariant
| cryptography
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/130338
**Description:**
We give explicit formulas for the number of distinct elliptic curves over a finite field (up to isomorphism over the algebraic closure of the ground field) in several families of curves of cryptograph
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**Reviewed:**
**Date:** 2010
**Subject Keyword:**
080200 Computation Theory and Mathematics
| polynomial maps
| pseudorandom number generators
| hashing
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/130893
**Description:**
Dynamical systems generated by iterations of multivariate polynomials with slow degree growth have proved to admit good estimates of exponential sums along their orbits which in turn lead to rather st
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**Reviewed:**
**Date:** 2010
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/128917
**Description:**
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets
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**Reviewed:**

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