Abstract
Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an approach for generating a pseudo-random multi-value sequence (including a binary sequence) by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field. All our previous sequences are defined over the prime field, whereas, proposed sequence in this paper is defined over the sub extension field. Thus, it’s a new and innovative perception to consider the sub extension field during the sequence generation procedure. By considering the sub extension field, two notable outcomes are: proposed sequence holds higher linear complexity and more uniform distribution of bit patterns compared to our previous work which defined over the prime field. Additionally, other important properties of the proposed multi-value sequence such as period, autocorrelation, and cross-correlation are theoretically shown along with some experimental results.
Highlights
Sequences of numbers generated by using an algorithm are referred to as a pseudo-random sequence
Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography
This paper proposes an approach for generating a pseudo-random multi-value sequence by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field
Summary
Sequences of numbers generated by using an algorithm are referred to as a pseudo-random sequence. Our previous work on binary sequence [13] uses a primitive polynomial, trace function, and Legendre symbol to generate a new variety of pseudo-random binary sequence. Our previous works on multi-value sequence [14] [15] utilizes a primitive polynomial, trace function, and power residue symbol over odd characteristic field. The authors in this paper proposed a multi-value sequence (including a binary sequence) by applying a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field q. The authors recently started to consider the sub extension field q during the sequence generation procedure, whereas, almost all our previous works on pseudo-random sequence [13] [14] [15] are considered in the prime field p.
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