One-Way Function Generation via Mutual Hiding Success Criteria
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Solution Overview
Problem
Current one-way functions used in cryptography are assumed to be one-way but lack provable security, leading to potential weaknesses and a lack of a provable cryptographic hash function, which is a longstanding open problem in computational complexity theory.
Innovation Solution
A method is developed to create a one-way function by selecting original computation tasks with predefined success criteria, combining them using bitwise XOR operations, and randomly shuffling elements to form a computation task, which is represented by a polynomial with randomly chosen coefficients, and using Rivest's Rotated XOR operations to hide the success criteria within a Merkle binary tree.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If current assumed one-way functions are used in cryptography, then cryptographic operations can be performed, but they lack provable security and may reveal weaknesses
Solution Approach 1:
The patent segments the one-way function into multiple independent computation tasks (e.g., sorting tasks, subset-sum tasks). Each task has its own success criterion that is hidden separately. By dividing the function into segments, the system achieves provable security because each segment's hardness can be independently verified against known computational problems, eliminating the reliance on unproven assumptions about a single monolithic function.
Solution Approach 2:
The patent creates a composite one-way function by combining multiple different computation tasks (sorting, subset-sum, polynomial evaluation) with different success criteria. This composite structure leverages the proven hardness of multiple distinct computational problems, creating a more robust cryptographic primitive that inherits security guarantees from each component task rather than relying on a single unproven assumption.
2Reliability
If multiple computation tasks are combined with mutual hiding of success criteria, then cryptographic strength is enhanced, but device complexity increases
Solution Approach 1:
The patent employs universal computational frameworks that can handle multiple types of tasks (sorting, subset-sum, polynomial evaluation) through a common structure. The success criteria are all based on finding specific computational properties (orderings, subset sums, polynomial coefficients), and the mutual hiding mechanism works uniformly across different task types. This universality reduces the operational complexity despite the multi-task structure, as the same cryptographic principles apply to each task type.
Data Source
AI summary
A method for creating a one-way function from a computation problem instances with a predefined success criteria, based on mutual hiding of the success criteria, comprising the steps of selecting at least a first and a second original computation tasks, each having an original corresponding success criterion; applying a function (such as a bitwise XOR operation) over both original corresponding success criteria, to form a single combined success criterion for a mutual computation task being a combination of the at least a first and a second original computation tasks; outputting the original computation tasks along with the combined success criterion, while excluding the original corresponding success criteria.