CA2631924A1 - Extending a repetition period of a random sequence - Google Patents

Extending a repetition period of a random sequence Download PDF

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Publication number
CA2631924A1
CA2631924A1 CA002631924A CA2631924A CA2631924A1 CA 2631924 A1 CA2631924 A1 CA 2631924A1 CA 002631924 A CA002631924 A CA 002631924A CA 2631924 A CA2631924 A CA 2631924A CA 2631924 A1 CA2631924 A1 CA 2631924A1
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Prior art keywords
residue values
rns
rns residue
random number
digits
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Granted
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CA002631924A
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French (fr)
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CA2631924C (en
Inventor
Alan J. Michaels
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Harris Corp
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Harris Corp
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Publication of CA2631924A1 publication Critical patent/CA2631924A1/en
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Publication of CA2631924C publication Critical patent/CA2631924C/en
Expired - Fee Related legal-status Critical Current
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Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/58—Random or pseudo-random number generators
    • G06F7/582—Pseudo-random number generators
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
    • G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
    • G06F7/729—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic using representation by a residue number system
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/76—Arrangements for rearranging, permuting or selecting data according to predetermined rules, independently of the content of the data

Abstract

A method is provided for extending a sequence repetition period of a random number generator in systems based on the availability of random sequences. The method includes performing RNS arithmetic operations to express a random number in a sequence as RNS residue values. Each generated random number has a value between zero and n!-1. The method also includes converting each of the RNS residue values to a relatively prime base number system so that each of the RNS residue values includes at least one digit. The method further includes generating an arbitrary permutation ordering of output sequence numbers using a select combination of digits associated with each of the RNS residue values. The arbitrary permutation ordering is applied to a cyclic structure having n elements. Each of the n elements has an associated output sequence number.

Claims (10)

1. A method for extending a sequence repetition period of a random number generator in a system based on the availability of a random sequence, comprising:

performing a plurality of residue number system (RNS) arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values;

converting each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit; and generating an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure.
2. The method according to claim 1, further comprising selecting said cyclic structure to have n elements and selecting said random number to have a value which can range between zero and n!-1.
3. The method according to claim 2, further comprising associating each of said plurality of output sequence numbers with a respective element of said n elements.
4. The method according to claim 1, further comprising calculating said plurality of RNS residue values using relatively prime numbers as moduli, wherein said moduli are determined by determining a decimal number defined by n! as a product of relatively prime numbers.
5. The method according to claim 1, wherein said converting step further comprises converting each of said plurality of RNS residue values to a different relatively prime number system.
6. The method according to claim 1, further comprising choosing said select combination of digits so that a range of values which can be determined by said digits is equal to a number of available unselected elements in said cyclic structure.
7. The method according to claim 1, further comprising using a value of said select combination of digits to select an available unselected element in said cyclic structure.
8. The method according to claim 1, wherein said generating step further comprises using a Chinese Remainder Theorem to combine at least two digits associated with at least two RNS residue values to obtain a digit having a different number base than said at least two digits.
9. The method according to claim 8, further comprising using said digit having a different number base to select an available unselected element in said cyclic structure.
10. A ring generator, comprising:

a computing means configured for performing a plurality of RNS
arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values;

a converting means configured for converting each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit; and a permutation means configured for generating an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure.
CA2631924A 2007-05-22 2008-05-21 Extending a repetition period of a random sequence Expired - Fee Related CA2631924C (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US11/751,783 2007-05-22
US11/751,783 US7921145B2 (en) 2007-05-22 2007-05-22 Extending a repetition period of a random sequence

Publications (2)

Publication Number Publication Date
CA2631924A1 true CA2631924A1 (en) 2008-11-22
CA2631924C CA2631924C (en) 2012-02-07

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Family Applications (1)

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CA2631924A Expired - Fee Related CA2631924C (en) 2007-05-22 2008-05-21 Extending a repetition period of a random sequence

Country Status (4)

Country Link
US (1) US7921145B2 (en)
EP (1) EP2000900B1 (en)
JP (1) JP4559505B2 (en)
CA (1) CA2631924C (en)

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Publication number Publication date
EP2000900B1 (en) 2015-04-29
JP4559505B2 (en) 2010-10-06
CA2631924C (en) 2012-02-07
EP2000900A3 (en) 2009-03-11
US20080294710A1 (en) 2008-11-27
EP2000900A2 (en) 2008-12-10
JP2009003925A (en) 2009-01-08
US7921145B2 (en) 2011-04-05

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