Collapsing Hash Construction from Semi-Regular PQ-CRHFs
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Solution Overview
Problem
Existing post-quantum collision resistant hash functions (PQ-CRHFs) are insufficient for applications requiring collapsing resistance, as they are often non-collapsing and rely on complex oracles or untested conjectures, and standard-model proofs require Learning With Errors (LWE), while symmetric hash functions like SHA2 or SHA3 lack evidence for collapsing.
Innovation Solution
Constructing a collapsing hash function H′ from any PQ-CRHF H that satisfies a mild structural condition called semi-regularity, which allows for compiling non-collapsing hash functions into collapsing ones using Merkle-Damgård domain extension and assuming semi-regularity or optimal collision resistance, and applying this to hash functions based on LPN, expanders, or group actions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard-model proofs of collapsing hashes are constructed, then post-quantum security is improved, but the construction requires Learning With Errors (LWE) which increases complexity
Solution Approach 1:
The patent introduces a Merkle-Damgård domain extension as an intermediary mechanism that transforms a simple post-quantum collision-resistant hash function into a collapsing hash function. This intermediary construction allows the system to achieve post-quantum security without directly requiring complex LWE-based constructions, thereby resolving the contradiction between security reliability and construction complexity.
Solution Approach 2:
The patent segments the hash function construction into two distinct components: a base post-quantum collision-resistant hash function (which can be simpler and more efficient) and a Merkle-Damgård domain extension layer (which provides the collapsing property). This segmentation allows each component to be optimized independently, reducing overall complexity while maintaining security.
2Adaptability or versatility
If collapsing hash functions are constructed from PQ-CRHF, then applications requiring collapsing resistance are enabled, but the requirement of semi-regularity condition limits applicability
Solution Approach 1:
The patent changes the parameter perspective by introducing the semi-regularity condition as a verifiable property of the hash function's output distribution. Rather than imposing complex structural constraints on the hash function itself, the approach checks whether the output satisfies a statistical regularity condition, which is a more flexible and easier-to-verify parameter that enables broader application compatibility.
3Productivity
If non-collapsing hash functions like SHA2 or SHA3 are used, then efficiency is improved, but they lack evidence for collapsing resistance
Solution Approach 1:
The patent applies preliminary action by pre-processing the output of efficient but non-collapsing hash functions (like SHA2 or SHA3) through a Merkle-Damgård domain extension. This preliminary transformation step converts the efficient but insecure hash output into a form that provides collapsing resistance, allowing the system to maintain high computational efficiency while achieving the required security property.
Data Source
AI summary
Systems, methods, and computer-readable media for creating a quantum-secure hash of an m-bit input are disclosed. The disclosure relates to the first statistically hiding post-quantum commitments and post-quantum succinct arguments (of knowledge) under the same assumptions. Results are obtained by a general theorem which shows how to construct a collapsing hash H′ from a post-quantum collision-resistant hash function H, regardless of whether or not H itself is collapsing, assuming H satisfies a certain regularity condition we call “semi-regularity”.