### Abstract

Recently, Goubin, Mauduit, Rivat and Sárközy have given three constructions for large families of binary sequences. In each of these constructions the sequence is defined by modulo congruences where p is a prime number. In this paper the three constructions are extended to the case when the modulus is of the form pq where p, q are two distinct primes not far apart (note that the well-known Blum-Blum-Shub and RSA constructions for pseudorandom sequences are also of this type). It is shown that these modulo pq constructions also have certain strong pseudorandom properties but, e.g., the ("long range") correlation of order 4 is large (similar phenomenon may occur in other modulo pq constructions as well).

Original language | English |
---|---|

Pages (from-to) | 75-107 |

Number of pages | 33 |

Journal | Periodica Mathematica Hungarica |

Volume | 51 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 2005 |

### Fingerprint

### Keywords

- Additive character
- Binary sequence
- Correlation
- Pseudo-random

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Modular constructions of pseudorandom binary sequences with composite moduli.** / Rivat, Joël; Sárközy, A.

Research output: Contribution to journal › Article

*Periodica Mathematica Hungarica*, vol. 51, no. 2, pp. 75-107. https://doi.org/10.1007/s10998-005-0031-7

}

TY - JOUR

T1 - Modular constructions of pseudorandom binary sequences with composite moduli

AU - Rivat, Joël

AU - Sárközy, A.

PY - 2005/12

Y1 - 2005/12

N2 - Recently, Goubin, Mauduit, Rivat and Sárközy have given three constructions for large families of binary sequences. In each of these constructions the sequence is defined by modulo congruences where p is a prime number. In this paper the three constructions are extended to the case when the modulus is of the form pq where p, q are two distinct primes not far apart (note that the well-known Blum-Blum-Shub and RSA constructions for pseudorandom sequences are also of this type). It is shown that these modulo pq constructions also have certain strong pseudorandom properties but, e.g., the ("long range") correlation of order 4 is large (similar phenomenon may occur in other modulo pq constructions as well).

AB - Recently, Goubin, Mauduit, Rivat and Sárközy have given three constructions for large families of binary sequences. In each of these constructions the sequence is defined by modulo congruences where p is a prime number. In this paper the three constructions are extended to the case when the modulus is of the form pq where p, q are two distinct primes not far apart (note that the well-known Blum-Blum-Shub and RSA constructions for pseudorandom sequences are also of this type). It is shown that these modulo pq constructions also have certain strong pseudorandom properties but, e.g., the ("long range") correlation of order 4 is large (similar phenomenon may occur in other modulo pq constructions as well).

KW - Additive character

KW - Binary sequence

KW - Correlation

KW - Pseudo-random

UR - http://www.scopus.com/inward/record.url?scp=30844454452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30844454452&partnerID=8YFLogxK

U2 - 10.1007/s10998-005-0031-7

DO - 10.1007/s10998-005-0031-7

M3 - Article

AN - SCOPUS:30844454452

VL - 51

SP - 75

EP - 107

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

SN - 0031-5303

IS - 2

ER -