RSA Key Vulnerability Detection via Product Tree GCD Analysis
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for determining whether encryption keys are vulnerable to exploitation, particularly due to deficiencies in pseudorandom number generation, are inefficient and burdensome as the number of publicly available keys grows exponentially, with known techniques requiring either flawed assumptions or computationally intractable calculations.
Innovation Solution
A system that receives and processes encryption key data to identify duplicate keys and calculate greatest common divisors, using a batch-comparison technique to build and update a product tree, enabling efficient detection of vulnerable keys by factoring them into prime factors and generating alerts for compromised keys.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional key vulnerability detection methods are used, then detection capability is provided, but computational burden becomes intractable as the number of keys grows
Solution Approach 1:
The patent segments the key detection process into two distinct phases: an offline phase where a product tree is constructed from a database of keys, and an online phase where new keys are detected by comparing against the pre-built tree. This segmentation allows the computationally intensive work to be done offline, making online detection efficient and scalable.
Solution Approach 2:
The patent performs preliminary actions by pre-processing a large database of keys into a product tree structure before actual detection is needed. This pre-computation stores intermediate results that can be quickly queried during online operation, eliminating the need to re-process all keys for each detection task.
2Measurement precision
If exhaustive key comparison is performed, then accurate vulnerability detection is achieved, but processing time becomes prohibitive for large key volumes
Solution Approach 1:
The patent divides the key base into a hierarchical product tree structure where keys are grouped and intermediate products are pre-computed. This segmentation allows the system to check multiple keys simultaneously through tree traversal rather than performing exhaustive pairwise comparisons, maintaining accuracy while dramatically reducing processing time.
Solution Approach 2:
The patent merges multiple key comparisons into a single tree traversal operation. By combining the detection of multiple keys through the shared product tree structure, the system achieves batch processing efficiency while maintaining individual key detection accuracy.
3Adaptability or versatility
If the database of encryption keys is continuously updated, then detection coverage is improved, but system complexity increases
Solution Approach 1:
The patent performs preliminary organization of keys into a product tree structure that is designed to accommodate updates. When new keys are added, the system can efficiently integrate them into the existing tree structure without re-processing the entire database, maintaining scalability while improving detection coverage.
Solution Approach 2:
The patent creates a dynamic system where the product tree can be efficiently updated as new keys are discovered or added to the database. The tree structure allows for incremental updates rather than requiring complete reconstruction, enabling the system to adapt to growing key volumes while maintaining manageable complexity.
Data Source
AI summary
Techniques for determining whether a public encryption key is vulnerable as the result of deficiencies in pseudorandom number generation algorithms are provided. In some embodiments, a system may compile a database of cryptographic information received from a plurality of sources, including databases, and network traffic monitoring tools. RSA public keys extracted from the cryptographic information may be stored in an organized database in association with corresponding metadata. The system may construct a product tree from all unique collected RSA keys, and may then construct a remainder tree from the product tree, wherein each output remainder may be determined to be a greatest common divisor of one of the RSA keys against all other unique RSA keys in the database. The system may then use the greatest common divisors to factor one or more of the RSA keys and to determine that the factored keys are vulnerable to being compromised.