Random Number Entropy Enhancement via S-Box Mapping and XOR Combination
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Solution Overview
Problem
Current cryptographic applications require high-entropy random numbers, but existing noise sources often fall short in achieving the desired level of randomness, particularly in generating random numbers with perfect per-bit entropy of 1.
Innovation Solution
The method involves combining multiple random processes through mapping and XOR operations using S-boxes and XOR gates to increase the entropy of random numbers, allowing for the use of lower-entropy individual random numbers while achieving higher combined entropy suitable for cryptographic security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If multiple random processes are combined through mapping and XOR operations, then the entropy of random numbers is increased, but the device complexity increases
Solution Approach 1:
The system divides the random number generation task into multiple independent random processes (e.g., multiple noise sources), each contributing a portion of the total entropy. This segmentation allows the system to achieve high overall entropy while keeping individual components simpler and more manageable.
Solution Approach 2:
The patent combines multiple random processes through XOR operations and mapping functions to create a unified random number output with higher entropy. By merging the outputs of multiple independent random sources, the system achieves the desired entropy level while distributing the complexity across multiple components.
2Reliability
If S-boxes are used to map random numbers, then the entropy is increased and cryptographic security is improved, but the processing time and computational cost increase
Solution Approach 1:
The system performs preliminary mapping operations using S-boxes on individual random numbers before combining them through XOR operations. This preliminary action prepares the random numbers in advance, allowing the main combining operation to proceed more efficiently and reducing overall processing time.
Solution Approach 2:
The patent uses S-boxes to transform the probability distribution parameters of the random numbers, mapping them to new distributions that have higher entropy. This parameter transformation achieves the desired cryptographic security properties while controlling the computational overhead through efficient S-box implementation.
Data Source
AI summary
Approaches proposed in the present case relate to the process of increasing the entropy of a random number, wherein a plurality of random processes each provide a random number, the plurality of random numbers are linked to form a combined random number, and at least one of the random numbers has previously been mapped to another random number.