Pseudorandom Sequence Complexity and Generation Techniques
Summary
Pseudorandom sequences form the backbone of modern cryptography, secure communications and Monte Carlo simulation, requiring deterministic constructions that mimic true randomness under stringent resource constraints. Complexity measures such as linear, maximum-order, Lempel–Ziv and expansion complexities evaluate the unpredictability and structural richness of sequences, while correlation and cross-correlation metrics gauge susceptibility to statistical or algebraic attacks. Generation techniques range from classical linear feedback shift registers and combinatorial designs based on primitive polynomials to more recent approaches using discrete logarithms, morphic and automatic sequence frameworks and algebraic function fields. Balancing maximal complexity, efficient hardware or software implementation and provable security properties remains a central challenge, driving ongoing research into novel algebraic and analytic constructions.
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Pseudorandom Sequence Complexity and Generation Techniques publication trend
The graph below shows the total number of articles in pseudorandom sequence complexity and generation techniques across all publications each year (not limited to Nature Index journals).
Technical terms
Pseudorandom sequence: A deterministic sequence designed to exhibit statistical properties characteristic of true randomness.
Linear complexity: The length of the shortest linear feedback shift register capable of reproducing a given sequence.
Maximum-order complexity: The minimal order of a recurrence relation required to generate all subsequences up to a specified length.
Correlation measure: A quantitative indicator of similarity between a sequence and its shifts or between distinct sequences, reflecting predictability.
Family complexity: The smallest pattern length such that every possible pattern of that length appears in at least one sequence within a family.
References
- A Survey on Complexity Measures for Pseudo-Random Sequences. Cryptography (2024).
- Maximum-Order Complexity and Correlation Measures. Cryptography (2017).
- Complexity of automatic sequences. Information and Computation (2022).
- Binary sequences and lattices constructed by discrete logarithms. AIMS Mathematics (2022).
- On the correlation of $ k $ symbols. AIMS Mathematics (2024).
- Families of sequences with good family complexity and cross-correlation measure. AIMS Mathematics (2025).
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