Chaotic Sequence Generator Using RNS and Lookup Tables
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Solution Overview
Problem
Existing chaotic communications systems face challenges with low throughput due to cumbersome synchronization of chaotic numerical sequences and the need for rapid updating of state information, particularly in scenarios where devices need to synchronize at arbitrary past or future states.
Innovation Solution
The method involves selecting polynomial equations with chaotic properties, using residue number system (RNS) arithmetic operations, and a variable 'v' defined by a mathematical expression to accelerate or decelerate chaotic sequence generation, allowing for instantaneous synchronization of chaotic sequences across devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional chaotic sequence generation methods are used, then the system maintains deterministic chaotic evolution, but the throughput is low due to cumbersome synchronization and frequent state updates
Solution Approach 1:
The patent pre-computes and stores chaotic sequence values in lookup tables before they are needed. By preparing the chaotic sequences in advance and storing them in memory, the system eliminates the need for real-time computation and complex synchronization during operation, thereby increasing throughput while reducing operational complexity
Solution Approach 2:
The patent uses lookup tables that contain pre-generated chaotic sequence values. Instead of computing chaotic sequences in real-time through complex iterative processes, the system copies pre-computed values from the lookup tables, significantly reducing computational complexity and improving throughput
2Reliability
If chaotic state information is updated frequently to maintain synchronization, then the synchronization accuracy is improved, but the user data throughput is limited
Solution Approach 1:
The patent pre-computes chaotic sequences and stores them in lookup tables with known starting points and lengths. This allows the system to rapidly jump to any synchronization point without iterative updates, maintaining synchronization accuracy while eliminating the need for frequent state updates that would otherwise limit data throughput
Solution Approach 2:
The lookup tables are designed to be self-sufficient, containing all necessary chaotic sequence information with embedded synchronization markers. The system can independently locate and synchronize to any point in the sequence without requiring continuous communication or coordination, thereby maintaining reliability while maximizing throughput
3Reliability
If a chaotic signal with near infinite repetition period is used, then the security and unpredictability are enhanced, but the ability to rapidly synchronize to arbitrary states is degraded
Solution Approach 1:
The patent divides the long-period chaotic sequence into multiple segments stored in lookup tables, each segment containing a portion of the chaotic sequence with known starting points. This segmentation allows the system to rapidly jump to any segment and achieve synchronization without compromising the overall long-period security characteristics of the chaotic signal
Solution Approach 2:
The patent pre-organizes chaotic sequence data in lookup tables with known starting points and structured formatting. This preliminary organization enables rapid synchronization to arbitrary states by simply pointing to the appropriate table entry, while the actual chaotic sequence maintains its near-infinite period for security
Data Source
AI summary
A method for generating an accelerated and/or decelerated chaotic sequence. The method involves selecting a plurality of polynomial equations constructed from an acc-dec variable v. The method also involves selecting a value for the acc-dec variable v for advancing or stepping back a chaotic sequence generation by at least one cycle at a given time. The method further involves using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations using the acc-dec variable v. The solutions iteratively computed and expressed as RNS residue values. The method involves determining a series of digits in a weighted number system based on the RNS residue values.