Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers

Alina Ostafe

doi:10.1007/978-3-642-13797-6_5

Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers

Alina Ostafe^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

9 Citations (Scopus)

Abstract

In this paper we study a new class of dynamical systems generated by iterations of a class of multivariate permutation polynomial systems. Using the same techniques studied previously for other generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit stronger estimates than in the general case and thus can be of use for pseudorandom number generation. We also prove a nontrivial bound "on average" over all initial values V is an element of F(p)(m) on the discrepancy for pseudorandom vectors generated by these iterations.

Original language	English
Title of host publication	Arithmetic of finite fields
Subtitle of host publication	third international workshop, WAIFI 2010, proceedings
Editors	M. Anwar Hasan, Tor Helleseth
Place of Publication	Berlin; Heidelberg
Publisher	Springer, Springer Nature
Pages	62-72
Number of pages	11
ISBN (Print)	9783642137969
DOIs	https://doi.org/10.1007/978-3-642-13797-6_5
Publication status	Published - 2010
Externally published	Yes
Event	3rd International Workshop on Arithmetic of Finite Fields - Istanbul, Turkey Duration: 27 Jun 2010 → 30 Jun 2010

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	6087
ISSN (Print)	0302-9743

Conference

Conference	3rd International Workshop on Arithmetic of Finite Fields
Country/Territory	Turkey
City	Istanbul
Period	27/06/10 → 30/06/10

Keywords

Nonlinear pseudorandom number generators
triangular polynomial systems
exponential sums
discrepancy
NUMBERS

Access to Document

10.1007/978-3-642-13797-6_5

Cite this

Ostafe, A. (2010). Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers. In M. A. Hasan, & T. Helleseth (Eds.), Arithmetic of finite fields: third international workshop, WAIFI 2010, proceedings (pp. 62-72). (Lecture Notes in Computer Science; Vol. 6087). Springer, Springer Nature. https://doi.org/10.1007/978-3-642-13797-6_5

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title = "Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers",

abstract = "In this paper we study a new class of dynamical systems generated by iterations of a class of multivariate permutation polynomial systems. Using the same techniques studied previously for other generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit stronger estimates than in the general case and thus can be of use for pseudorandom number generation. We also prove a nontrivial bound {"}on average{"} over all initial values V is an element of F(p)(m) on the discrepancy for pseudorandom vectors generated by these iterations.",

keywords = "Nonlinear pseudorandom number generators, triangular polynomial systems, exponential sums, discrepancy, NUMBERS",

author = "Alina Ostafe",

year = "2010",

doi = "10.1007/978-3-642-13797-6_5",

language = "English",

isbn = "9783642137969",

series = "Lecture Notes in Computer Science",

publisher = "Springer, Springer Nature",

pages = "62--72",

editor = "Hasan, {M. Anwar} and Tor Helleseth",

booktitle = "Arithmetic of finite fields",

address = "United States",

note = "3rd International Workshop on Arithmetic of Finite Fields ; Conference date: 27-06-2010 Through 30-06-2010",

}

Ostafe, A 2010, Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers. in MA Hasan & T Helleseth (eds), Arithmetic of finite fields: third international workshop, WAIFI 2010, proceedings. Lecture Notes in Computer Science, vol. 6087, Springer, Springer Nature, Berlin; Heidelberg, pp. 62-72, 3rd International Workshop on Arithmetic of Finite Fields, Istanbul, Turkey, 27/06/10. https://doi.org/10.1007/978-3-642-13797-6_5

Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers. / Ostafe, Alina.
Arithmetic of finite fields: third international workshop, WAIFI 2010, proceedings. ed. / M. Anwar Hasan; Tor Helleseth. Berlin; Heidelberg: Springer, Springer Nature, 2010. p. 62-72 (Lecture Notes in Computer Science; Vol. 6087).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

TY - GEN

T1 - Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers

AU - Ostafe, Alina

PY - 2010

Y1 - 2010

N2 - In this paper we study a new class of dynamical systems generated by iterations of a class of multivariate permutation polynomial systems. Using the same techniques studied previously for other generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit stronger estimates than in the general case and thus can be of use for pseudorandom number generation. We also prove a nontrivial bound "on average" over all initial values V is an element of F(p)(m) on the discrepancy for pseudorandom vectors generated by these iterations.

AB - In this paper we study a new class of dynamical systems generated by iterations of a class of multivariate permutation polynomial systems. Using the same techniques studied previously for other generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit stronger estimates than in the general case and thus can be of use for pseudorandom number generation. We also prove a nontrivial bound "on average" over all initial values V is an element of F(p)(m) on the discrepancy for pseudorandom vectors generated by these iterations.

KW - Nonlinear pseudorandom number generators

KW - triangular polynomial systems

KW - exponential sums

KW - discrepancy

KW - NUMBERS

U2 - 10.1007/978-3-642-13797-6_5

DO - 10.1007/978-3-642-13797-6_5

M3 - Conference proceeding contribution

SN - 9783642137969

T3 - Lecture Notes in Computer Science

SP - 62

EP - 72

BT - Arithmetic of finite fields

A2 - Hasan, M. Anwar

A2 - Helleseth, Tor

PB - Springer, Springer Nature

CY - Berlin; Heidelberg

T2 - 3rd International Workshop on Arithmetic of Finite Fields

Y2 - 27 June 2010 through 30 June 2010

ER -

Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers

Abstract

Publication series

Conference

Keywords

Access to Document

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Cite this