Punctured Ring Generator Mixed Radix Conversion
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Solution Overview
Problem
Conventional ring generators in cryptographic systems are computationally inefficient, resource-intensive, and have deterministic orbits that can be easily identified, making them unsuitable for cryptographic applications where masking is necessary.
Innovation Solution
A cryptographic system utilizing a punctured ring structure and mixed radix conversion to produce a random number sequence in a second number base, free from statistical artifacts, by removing specific elements from the ring structure and employing a combination of Galois fields with mutually prime characteristics, ensuring a uniform or non-uniform distribution as needed, and incorporating a truncation and size conversion mechanism.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a conventional ring generator is used in a cryptographic system, then the structure is simple and produces exhaustive outputs, but the computational efficiency is poor and hardware resources are heavily consumed
Solution Approach 1:
The patent extracts and removes specific elements from the ring structure to create a punctured ring generator. By removing n elements where n is determined by the remainder of the division of the first Galois field size by the second Galois field size, the system eliminates statistical artifacts while maintaining computational efficiency and reducing hardware resource consumption.
Solution Approach 2:
The patent changes the parameters of the ring generator by transitioning from a conventional structure to a punctured ring structure operating across two different Galois fields. This parameter change enables the system to achieve both computational efficiency and reduced hardware requirements while maintaining cryptographic security.
2Ease of operation
If a conventional ring generator is used, then the mapping is deterministic and easy to implement, but the orbits are highly deterministic and can be easily identified, compromising security
Solution Approach 1:
The patent removes specific elements from the ring structure to eliminate deterministic patterns. By puncturing the ring at strategically chosen positions determined by the mathematical relationship between the two Galois field sizes, the system breaks the deterministic orbits while maintaining implementation simplicity through the structured removal approach.
Solution Approach 2:
The patent introduces asymmetry by using two different Galois field characteristics (first and second mutually prime characteristics) and removing a specific number of elements n from the ring. This asymmetric structure creates non-uniform orbits that are more resistant to cryptographic analysis while keeping the implementation straightforward through the defined mathematical relationship.
3Productivity
If lookup table operations are performed in the finite field GF[M], then the ring generator can produce outputs, but the hardware resources are heavily consumed
Solution Approach 1:
The patent reduces hardware resources by extracting and removing unnecessary elements from the ring structure. The punctured ring generator requires fewer lookup table operations and less hardware infrastructure while maintaining the capability to generate secure random number sequences through the optimized structure operating across two Galois fields.
Solution Approach 2:
The patent changes the operational parameters by using a punctured ring structure with reduced element count and operating across two mutually prime Galois fields instead of a single large field. This parameter optimization maintains output generation capability while significantly reducing the quantity of hardware resources required.
Data Source
AI summary
A cryptographic system (CS) is provided. The CS (800) comprises a data stream receiving means (DSRM), a generator (702), a mixed radix converter (MRC) and an encryptor (908). The DSRM (902) is configured to receive a data stream (DS). The generator is configured to selectively generate a random number sequence (RNS) utilizing a punctured ring structure. The MRC (704) is coupled to the generator and configured to perform a mixed radix conversion to convert the RNS from a first number base to a second number base. The encryptor is coupled to the DSRM and MRC. The encryptor is configured to generate an altered data stream by combining the RNS in the second number base with the DS. The punctured ring structure and the MRC are configured in combination to produce an RNS in the second number base which contains a priori defined statistical artifacts after the mixed radix conversion.