Multimodal Map Pseudo-Random Bit Generator for Secure Encryption
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Solution Overview
Problem
Existing pseudo-random bit generators, particularly those based on chaotic systems, face limitations in generating cryptographically secure sequences that can produce distinct encryption images each time the same key is used, and they often rely on multiple dynamic systems or uni-modal maps, which can be inefficient and insecure.
Innovation Solution
A pseudo-random bit generator utilizing a single discrete-time dynamic multimodal system (k-modal map) that iterates independently to produce multiple time series, which are then combined using XOR operations, allowing for efficient and secure encryption with a single key by varying the number of modals and thresholds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If multiple dynamic systems or uni-modal maps are used to generate pseudo-random sequences, then cryptographic security is improved, but device complexity increases
Solution Approach 1:
The patent combines multiple uni-modal maps into a single multi-modal map structure that integrates the functionality of multiple independent systems. By merging the mapping functions f1(x), f2(x), ..., fk(x) into one unified multi-modal map with multiple critical points, the system achieves the cryptographic security of multiple systems while reducing device complexity to a single integrated generator.
Solution Approach 2:
The multi-modal map serves multiple functions simultaneously: it generates multiple pseudo-random sequences through its different modes, provides cryptographic security through chaotic dynamics, and reduces system complexity by consolidating what would otherwise require multiple separate generators. Each mode of the multi-modal map can be configured to produce sequences with different statistical properties.
2Ease of operation
If a single key is used for encryption, then ease of operation is improved, but encryption quality deteriorates due to identical cipher images
Solution Approach 1:
The system uses dynamic control parameters and initial conditions within the multi-modal map that can vary between encryption operations. Even with the same key, the chaotic nature of the multi-modal map produces different pseudo-random sequences when control parameters or initial conditions are dynamically adjusted, ensuring different cipher images while maintaining simple key management.
Solution Approach 2:
The multi-modal map employs periodic switching between different modes or regions of the map during sequence generation. This periodic action within the single generator creates varying output patterns that prevent identical cipher images from the same key, while the overall structure remains simple and key-management-friendly.
Data Source
AI summary
The present invention is related with a computer-implemented method for generating a pseudo-random bit generator including the steps: a. Defining a multi-modal map by the equation: ƒβ=β(dr+1−x)(x−dr), x∈ℑr; b. Set the value of k∈+, and obtaining the values of βj, for j=from at least 1, to the final value k by the following equations: β1=4k; βj=(j)(β1); for 2≤j≤k; and taking the values of βj and split the space into 2j regions δ1j, to δ2jj which are determined by values κ1j to k(2j)−1j.