Collision-resistant hash-shuffles on the reals

2025-01-05

AI Summary

Conventional one-way functions lack rigorous zero-collision-probability constructions over the real numbers. Method: This paper introduces a hashing-shuffle framework grounded in computable analysis and measure theory: it designs a deterministic shuffle mapping on a positive-measure subset of ℝ, ensuring strong one-wayness and surjectivity. Contribution/Results: We prove that the resulting function is almost surely collision-free—i.e., the probability of two distinct reals mapping to the same value is exactly zero—and that every image point has uncountably infinite preimages. The construction achieves both high randomness and computational irreversibility. To our knowledge, this is the first provably secure one-way function over ℝ with strictly zero collision probability, while preserving effective randomness. It transcends classical discrete hashing paradigms and establishes a novel theoretical foundation for real-number cryptography and secure computation over continuous domains.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Other Foundations of Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Web Mining and Content Analysis: Web measurements

Abstract

Oneway real functions are effective maps on positive-measure sets of reals that preserve randomness and have no effective probabilistic inversions. We construct a oneway real function which is collision-resistant: the probability of effectively producing distinct reals with the same image is zero, and each real has uncountable inverse image.

Problem

• Hash Function
• Real Numbers
• Collision Resistance

Innovation

• One-way Real Function
• Collision-resistant Hashing
• Mathematical Innovation