Digital Chaotic Sequence Generation via RNS Arithmetic
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing cryptographic systems face challenges in generating true chaotic sequences digitally due to impractical wordwidths and arithmetic precision requirements, leading to the reliance on analog chaos generators that drift over time and produce complex pseudo-random sequences without true chaotic properties.
Innovation Solution
A cryptographic system utilizing a computing device and mapping device with residue number system (RNS) arithmetic operations to generate chaotic sequences through polynomial equations, employing a feedback mechanism and Chinese Remainder Theorem for digital chaos generation, ensuring irreducible polynomial equations and chaotic properties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If analog chaotic circuits are used to generate chaotic sequences, then chaotic properties are achieved, but parameter drift occurs over time
Solution Approach 1:
The patent replaces analog chaotic circuits with a digital implementation using a feedback shift register and non-linear function. This substitution eliminates the parameter drift inherent in analog systems while preserving chaotic properties through deterministic digital operations modulo 2^N.
Solution Approach 2:
The patent changes the fundamental parameter representation from continuous analog values to discrete digital values modulo 2^N. This parameter transformation allows the system to maintain chaotic behavior through digital arithmetic operations while avoiding the drift problems of analog implementations.
2Measurement precision
If digital pseudo-random number generators are used, then arithmetic precision is improved, but true chaotic properties are lost
Solution Approach 1:
The patent introduces dynamic non-linear feedback into the digital system through the recurrence relation S(n) = f(S(n-1)) where f is a non-linear function. This dynamic element creates true chaotic behavior with sensitive dependence on initial conditions, distinguishing it from static pseudo-random generators.
Solution Approach 2:
The patent implements a feedback mechanism where the output of the non-linear function is fed back as the input for the next iteration. This feedback loop creates the sensitive dependence on initial conditions characteristic of chaotic systems, ensuring true chaotic properties while maintaining digital precision.
3Reliability
If high arithmetic precision is used to achieve digital chaos, then chaotic properties are improved, but device complexity increases
Solution Approach 1:
The patent segments the chaotic generation into discrete N-bit operations using modulo 2^N arithmetic. This segmentation allows chaotic behavior to be achieved with fixed-width registers and standard digital logic, reducing implementation complexity while maintaining chaotic properties through the modular arithmetic structure.
Data Source
AI summary
A cryptographic system (CS) is provided. The CS (500) is comprised of a data stream receiving device (DSRD), a chaotic sequence generator (CSG) and an encryptor. The DSRD (602) is configured to receive an input data stream. The CSG (300) includes a computing means (3020, . . . , 302N−1) and a mapping means (304). The computing means is configured to use RNS arithmetic operations to respectively determine solutions for polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The mapping means is configured to determine a series of digits in the weighted number system based on the RNS residue values. The encryptor is coupled to the DSRD and CSG. The encryptor is configured to generate a modified data stream by incorporating or combining the series of digits with the input data stream.