Cryptographic Key Determination via Quantum Annealing Optimization

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Determining cryptographic keys in an efficient and resource-conserving manner, particularly for symmetric-key cryptography algorithms, is challenging due to the computational hardness of deriving keys from plaintext and ciphertext.

Innovation Solution

A method is provided that involves transforming the cryptographic procedure into optimization problems, specifically mixed-integer linear programming (MILP) or quadratic unconstrained binary optimization (QUBO) problems, which can be solved using quantum annealing devices, allowing for the determination of cryptographic keys by analyzing intermediate relations and optimization expressions derived from cryptographic operations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If cryptographic key determination is performed using traditional computational methods, then the problem is computationally hard and resource-intensive, but the patent transforms it into an optimization problem solvable by quantum annealing devices achieving substantial computational speedup

Engineering Contradiction:

Improvecomputational speedupVSAvoidcomplexity of determining cryptographic key

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The patent replaces traditional computational methods with quantum annealing, substituting classical computational mechanics with quantum mechanical processes. The cryptographic key determination problem is transformed into a QUBO optimization problem that leverages quantum tunneling and energy minimization to achieve exponential speedup over classical approaches.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent changes the fundamental parameters of the problem by transforming cryptographic key determination from a direct computational search into an optimization problem with objective functions and constraints. This parameter transformation enables the use of quantum annealing by mapping discrete cryptographic operations into continuous optimization landscapes.

Inventive Principle:

Principle #35Parameter changes

2Measurement precision

If the cryptographic procedure is analyzed in detail with intermediate relations for each operation, then the accuracy of key determination improves, but the complexity of the optimization problem increases

Engineering Contradiction:

Improveaccuracy of cryptographic key determinationVSAvoidcomplexity of optimization problem

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent segments the cryptographic procedure into individual operations (SubBytes, ShiftRows, MixColumns, AddRoundKey) and formulates separate intermediate relations for each segment. This segmentation allows the complex cryptographic analysis to be broken down into manageable optimization constraints that can be systematically combined into the final QUBO problem.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent introduces intermediate relations as mediator variables that connect different cryptographic operations. These intermediate variables serve as bridges between plaintext, ciphertext, and the cryptographic key, enabling the formulation of optimization expressions that capture the relationships across multiple cryptographic rounds without directly exposing the key.

Inventive Principle:

Principle #24Intermediary (Mediator)

3Productivity

If quantum annealing is used to solve the optimization problem, then computational efficiency improves substantially, but the requirement for quantum processing devices increases

Engineering Contradiction:

Improvecomputational efficiencyVSAvoidapplicability to various cryptographic algorithms

Core Design Contradiction:

ProductivityVSAdaptability or versatility

Solution Approach 1:

The patent creates a universal framework that can analyze multiple symmetric cryptographic algorithms (AES, ARX-based ciphers, DES, 3DES) using the same QUBO formulation approach. The method is adaptable to different cryptographic procedures by modifying the intermediate relations and optimization expressions while maintaining the core quantum annealing solving mechanism.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS12126710B2Method for determining a cryptographic key, computer program, and data processing system

Publication Date: 2024.10.22 TERRA QUANTUM AG

AI summary

A method for determining a cryptographic key is carried out in a data processing system, and comprises: providing a plaintext and a ciphertext determined from the plaintext using a cryptographic key and a cryptographic procedure which comprises cryptographic operations; for each cryptographic operation of the cryptographic procedure, providing at least one intermediate relation which comprises an intermediate equation and/or an intermediate inequality; determining an optimization problem comprising: the plaintext and the ciphertext; at least one optimization expression assigned to a round of the cryptographic procedure; and optimization variables comprising state variables of the cryptographic procedure and a cryptographic key variable; wherein the at least one optimization expression is determined from the at least one intermediate relation and comprises at least one preceding state variable assigned to a preceding round. The method further comprises: solving the optimization problem and determining the cryptographic key from an optimizing value of the cryptographic key variable.