Mixed Radix Number Generator for Secure Communications
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Solution Overview
Problem
Existing ring generators in communications systems face inefficiencies in digital computation, are memory-intensive, and produce deterministic output sequences, making them vulnerable to frequency attacks, especially when the Galois characteristic P is a prime number or large, leading to statistical artifacts that can be used to re-engineer the sequence.
Innovation Solution
A mixed radix number generator is implemented, which generates a sequence of numbers by performing modulo P operations on a larger Galois field GF[M] that is relatively prime to P, distributing statistical artifacts evenly across all equivalence classes of GF[P], creating a pseudo-random sequence with chosen statistical characteristics that appear non-deterministic.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a ring generator uses a prime Galois characteristic P for computational efficiency, then the computation becomes more efficient in the digital domain, but the output sequence becomes highly deterministic and vulnerable to frequency attacks
Solution Approach 1:
The patent introduces a mixed-radix conversion process as an intermediary between the ring generator output and the final sequence. This conversion uses a modulus M that is composite (product of distinct primes) rather than prime, creating statistical artifacts that mask the deterministic pattern while maintaining computational efficiency. The intermediary conversion layer hides the underlying deterministic structure from frequency analysis attacks.
Solution Approach 2:
The patent changes the parameter from a prime Galois characteristic to a composite modulus M in the mixed-radix conversion. By using a composite M with distinct prime factors, the system creates a more complex statistical distribution pattern that appears random to frequency attackers while preserving the efficiency benefits of the original prime-based ring generator.
2Reliability
If the Galois characteristic P is chosen to be large for better statistical properties, then the sequence appears more random, but the lookup table operations become memory intensive
Solution Approach 1:
The patent segments the large Galois field GF[P] into a product of smaller fields by using a composite modulus M that is the product of distinct primes. This allows the system to work with smaller, more manageable field sizes in each component while achieving the statistical properties of a large field through the Chinese Remainder Theorem, thereby reducing memory requirements for lookup tables.
Solution Approach 2:
The patent transitions from a single large-dimensional Galois field to a multi-dimensional structure using composite modulus. Instead of working with one large field GF[P], the system uses a product of smaller fields, effectively moving the problem to a different dimensional representation that reduces memory footprint while maintaining statistical quality.
3Reliability
If mixed-radix conversion is applied to mask the output sequence, then statistical artifacts are introduced to prevent frequency attacks, but the conversion process itself becomes complex
Solution Approach 1:
The patent implements the mixed-radix conversion using the ring generator's own internal operations and outputs. The conversion process reuses the ring generator's computational resources and output structure, allowing the system to perform the masking function without requiring entirely separate complex conversion hardware. The ring generator essentially converts itself into the desired statistical distribution.
Solution Approach 2:
The patent merges the ring generator functionality with the mixed-radix conversion operations into a unified structure. By combining the sequence generation and statistical masking functions into a single integrated system, the patent reduces overall complexity compared to having separate independent components, while still achieving the security benefits of the conversion process.
Data Source
AI summary
A method is provided for masking a process used in generating a number sequence. The method includes generating a first sequence of numbers contained within a Galois field GF[M]. The method also includes performing a first modification to a first number in the first sequence of numbers. The first modification includes summing the first number with a result of a modulo P operation performed on a second number of the first sequence that proceeds the first number. M is relatively prime with respect to P. The method further includes performing a second modification to the first random number. The second modification is comprised of a modulo P operation. This second modification is performed subsequent to the first modification. The method includes repeating the first and second modification for a plurality of numbers comprising the first sequence of numbers to generate a second sequence of numbers.