[Paper Review] Binary Random Sequences Obtained From Decimal Sequences

Suresh B. Thippireddy|ArXiv.org|Sep 3, 2008

Chaos-based Image/Signal Encryption15 references3 citations

TL;DR

This paper proposes a novel method for generating binary random sequences by converting prime reciprocal fractions from decimal (base 10) to binary (base 2), analyzing their autocorrelation and cross-correlation properties. The approach yields sequences with favorable randomness characteristics, offering a new source for cryptographic applications with improved correlation properties compared to direct base-2 representation.

ABSTRACT

This paper presents a twist to the generation of binary random sequences by starting with decimal sequences. Rather than representing the prime reciprocal sequence directly in base 2, we first right the prime reciprocal in base 10 and then convert it into the binary form. The autocorrelation and cross-correlation properties of these binary random (BRD) sequences are discussed.

Motivation & Objective

• To explore an alternative method for generating binary random sequences using decimal representations of prime reciprocals.
• To evaluate the randomness quality of these sequences through autocorrelation and cross-correlation analysis.
• To determine whether converting decimal fractions to binary before sequence extraction improves correlation properties.
• To provide a new source of binary sequences suitable for cryptographic applications requiring high randomness.
• To compare the statistical properties of sequences derived from decimal-to-binary conversion with those from direct base-2 representation.

Proposed method

• The method begins with computing the reciprocal of a prime number in decimal (base 10) form.
• The resulting decimal fraction is then converted into its binary (base 2) representation.
• The binary digits are extracted sequentially to form a binary random sequence (BRD).
• Autocorrelation and cross-correlation properties of the BRD sequences are computed and analyzed.
• The sequences are evaluated for randomness using standard correlation metrics.
• The approach contrasts with traditional methods that directly represent prime reciprocals in base 2.

Experimental results

Research questions

• RQ1 Does converting decimal representations of prime reciprocals into binary yield binary sequences with favorable autocorrelation properties?
• RQ2 How do the cross-correlation properties of these BRD sequences compare to those of sequences generated via direct base-2 representation?
• RQ3 Can the decimal-to-binary conversion process produce sequences with improved randomness characteristics for cryptographic use?
• RQ4 What is the impact of the prime denominator on the correlation behavior of the resulting binary sequences?
• RQ5 Are there systematic patterns in the correlation properties across different prime reciprocals when converted via this method?

Key findings

• The binary sequences derived from decimal representations of prime reciprocals exhibit low autocorrelation side lobes, indicating good randomness.
• Cross-correlation values between different BRD sequences remain low, suggesting minimal interference and high orthogonality.
• The method produces sequences with more uniform correlation distribution compared to direct base-2 representation of the same reciprocals.
• Sequences generated from larger primes tend to show more favorable correlation properties, especially in cross-correlation.
• The transformation from decimal to binary preserves or enhances the inherent randomness of the original fraction, leading to improved statistical properties.
• The approach provides a viable alternative source of binary sequences with strong cryptographic potential due to their low correlation values.