Elliptic Curve Only Hash Function Collision Resistance
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Solution Overview
Problem
Existing hash functions, such as MuHash, do not provide a mechanism for building a collision-resistant hash function from scratch and rely on a pre-existing hash function, which limits their flexibility and security.
Innovation Solution
The Elliptic Curve Only Hash (ECOH) function generates a cryptographic hash value without relying on a pre-existing hash function, using an elliptic curve group and the identity function with padding to produce a collision-resistant hash, allowing for variable-input-length hash functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If MuHash is used to provide collision-free hashing with incrementality, then hashing efficiency is improved, but reliance on pre-existing hash functions limits flexibility and security
Solution Approach 1:
The patent extracts and removes the dependency on pre-existing hash functions from the MuHash paradigm. By using elliptic curve groups and the identity function with padding, the invention eliminates the need for external hash functions while maintaining collision resistance and incrementality, thus improving flexibility and security without sacrificing hashing efficiency
Solution Approach 2:
The patent introduces elliptic curve groups as an intermediary mathematical structure to replace the role of pre-existing hash functions. The identity function with padding serves as a mediator that transforms messages into elliptic curve points, enabling the construction of collision-resistant hash functions from scratch while preserving the incremental hashing capability
2Reliability
If a pre-existing hash function is used in MuHash, then collision resistance is achieved, but the security relies on assumptions about the pre-existing hash
Solution Approach 1:
The patent enables the hash function to be self-sufficient by using the identity function with padding directly on elliptic curve groups. This self-service approach eliminates the need to rely on external hash functions and their security assumptions, while maintaining collision resistance through the mathematical properties of elliptic curves and the discrete logarithm problem
Solution Approach 2:
The patent extracts and removes the dependency layer on pre-existing hash functions. By directly using elliptic curve groups with the identity function, the invention eliminates the need for security assumptions about external hash functions, reducing complexity while maintaining reliability through well-established cryptographic assumptions about elliptic curves
Data Source
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AI summary
Elliptic curve hash functions are provided which do not require a pre-existing hash function, such as that required by the MuHash. The elliptic curve hash functions can be built from scratch and are collision free and can be incremental. In one embodiment, rather than a pre-existing hash function, the identity function with padding is used; and in another embodiment, rather than a pre-existing hash function, a block cipher with a fixed non-secret key is used.