Merkle Tree Leaf Verification Path Segmentation
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Solution Overview
Problem
Merkle trees face inefficiencies in verification paths due to their size increasing with the number of leaves, leading to longer verification times and computational burdens in cryptographic schemes.
Innovation Solution
A method and processor system that determine verification paths for each leaf in a tree, ensuring path size independence from the number of leaves by using partial results and one-way functions, allowing for efficient and fast verification without re-computation of other leaf values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a traditional Merkle tree verification path is used, then the verification path provides complete authentication from leaf to root, but the size of the verification path increases linearly with the number of leaves, leading to longer verification times
Solution Approach 1:
The verification path is segmented into two independent parts: a partial result that depends only on other leaves (excluding the current leaf), and a final hash that combines the partial result with the current leaf value. This segmentation allows the verification path size to be constant rather than linear in the number of leaves, while still providing complete authentication.
Solution Approach 2:
The partial result is pre-computed from all leaves except the current one, and stored as part of the verification path. This preliminary action eliminates the need to re-compute portions of the verification path during verification, reducing verification time while maintaining authentication reliability.
2Reliability
If a traditional Merkle tree verification path is used, then the verification path ensures security by requiring all leaf values, but the computational burden increases with the number of leaves due to multiple hash algorithm calls
Solution Approach 1:
The computational workload is segmented such that the partial result (computed from m-1 leaves) is prepared once and stored, while verification only requires computing a single final hash combining the partial result with the current leaf value. This segmentation maintains security by requiring knowledge of all leaves while reducing computational complexity during verification to a constant number of hash operations.
3Loss of time
If the verification path size is reduced to improve verification speed, then verification time decreases, but the ability to prevent re-computation of other leaf values may be compromised
Solution Approach 1:
The partial result is pre-computed and stored as part of the verification path. This preliminary computation includes all necessary information from other leaves in a way that prevents re-computation of individual leaf values, while keeping the verification path size constant and verification time short.
Solution Approach 2:
The partial result acts as an intermediary that encapsulates information from all other leaves without exposing them. It serves as a mediator that allows verification of the current leaf while preventing re-computation of other leaf values, maintaining security without increasing verification path size.
Data Source
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AI summary
There is provided mechanisms for determining a verification path for each leaf of a tree. A method is performed by a tree manager processor. The method comprises acquiring leaf values of leaves of a tree. The method comprises determining a root value from a leaf to the root value of the leaves. The method comprises determining a verification path for each of the leaves. The verification path for each of the leaves is determined such that the size of each verification path is independent from the number of leaves. Each verification path comprises a partial result and a function that enables determination of said root value from its leaf value and said partial result. The partial result for the verification path for leaf is determined as a one-way function depending only on other leaves such that the verification path for leaf prohibits re-computation of any other leaf value from said partial result