Cryptographic Hash Preimage Determination via Quantum Annealing
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Solution Overview
Problem
Current methods for determining preimage elements of cryptographic hash functions are inefficient and resource-intensive, particularly for strong hash functions used in blockchain technology, where finding preimages is computationally hard and often impractical on available computers.
Innovation Solution
A method is provided to determine preimage elements by formulating an optimization problem using hash function relations and internal state variables, which are solved to find the preimage element efficiently, employing both classical and quantum processing devices to accelerate the computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exhaustive search or known preimage attacks are used on strong cryptographic hash functions, then the search for preimage elements can be completed, but the computation time and resource consumption become impractically high
Solution Approach 1:
The patent replaces classical computational mechanisms with quantum mechanical systems. Specifically, it uses quantum annealing to solve the preimage problem, transforming the computational approach from classical sequential processing to quantum parallel processing. The quantum system exploits superposition and tunneling effects to explore the solution space more efficiently, thereby reducing computation time while maintaining the cryptographic strength of the hash function.
Solution Approach 2:
The patent changes the computational parameters by formulating the preimage problem as an optimization problem with specific constraints. It transforms the cryptographic hash function evaluation into an energy minimization problem where the objective function represents the hash output and constraints enforce the preimage requirements. This parameter transformation enables the use of quantum annealing algorithms that can efficiently search for solutions.
2Productivity
If quantum annealing is used to solve the optimization problem, then the computation time is significantly reduced, but the device complexity increases due to requiring quantum processing devices
Solution Approach 1:
The patent segments the computational task into two distinct parts: a classical preprocessing stage that formulates the optimization problem by encoding the hash function relations and constraints, and a quantum processing stage that solves the formulated optimization problem using quantum annealing. This segmentation allows each part to be optimized independently, with the classical part handling problem formulation and the quantum part handling the computationally intensive search.
Solution Approach 2:
The patent introduces an intermediary optimization problem formulation that bridges the cryptographic hash function and the quantum annealing solver. The optimization problem serves as a mediator that translates the cryptographic preimage problem into a form suitable for quantum processing, with objective functions and constraints that encode the hash function behavior and preimage requirements.
Data Source
AI summary
A method for determining a preimage element of a cryptographic hash function includes providing an output value of a cryptographic hash function and hash function operations of the cryptographic hash function; for each of the hash function operations, determining at least one hash function relation, comprising an equation and/or an inequality; determining an optimization problem comprising: the output value, at least one constraint assigned to an iteration of the cryptographic hash function, and optimization variables comprising internal state variables of the cryptographic hash function and at least one preimage variable, wherein the at least one constraint is determined from the at least one hash function relation and comprises preceding internal state variables assigned to a preceding iteration; and solving the optimization problem and determining a preimage element of the cryptographic hash function from an optimizing value of the at least one preimage variable.