How do Diophantine equations form the basis of this new encryption?

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Diophantine Equations Underpin Novel "Unbreakable" Encryption Method

Two Singaporean brothers, Lim Meng Liang and Ken Lin, have developed a new encryption system, branded as "unbreakable," which leverages the unique properties of Diophantine equations. Their start-up, Aires Applied Quantum Technology, established in 2023, is pioneering this approach, which aims to provide robust security against the emerging threat posed by quantum computers. The core of their innovation lies in applying mathematical problems, historically known for lacking straightforward solutions, to the complex domain of data encryption.
The Nature of Diophantine Equations in Encryption

Diophantine equations are a class of mathematical problems that seek integer solutions. What makes them particularly intriguing for encryption is that many such equations are constructed to have no solutions, or an extremely limited and difficult-to-determine set of solutions. In the context of encryption, this inherent complexity and the difficulty in finding solutions are precisely what is being exploited. Instead of searching for a solution, the encryption process uses the structure and properties of these unsolvable or difficult-to-solve equations to obfuscate data. The sender generates specific keys based on these equations, and only a recipient possessing the corresponding inverse logic, derived from the same underlying mathematical principles, can decrypt the information. This makes brute-force attacks, which rely on systematically trying all possible solutions, computationally infeasible.
Application to Data Encryption via LionGuard

The practical implementation of this concept is realized through Aires' flagship product, the LionGuard mobile app. This subscription-based application encrypts files by employing sender-generated keys that are intrinsically linked to the Diophantine equation framework. When a user encrypts a file, the app generates a unique key derived from the specific Diophantine equation used in the process. This key is then used to scramble the data. To decrypt the file, the recipient must use a corresponding decryption key, which is essentially the inverse operation within the same mathematical system. This method is specifically designed to be resilient against future quantum computers. Current encryption standards, such as RSA, rely on the difficulty of factoring large prime numbers, a task that quantum computers are predicted to perform exponentially faster than classical computers, rendering these current methods vulnerable. The Diophantine equation approach, by contrast, is believed to be quantum-resistant because the computational problems involved are not susceptible to the same quantum algorithms that threaten existing encryption.
Quantum Threats and Resilience

The development of Aires' encryption technology is a direct response to the anticipated threat of quantum computing. Quantum computers, harnessing principles of quantum mechanics like superposition and entanglement, have the potential to solve certain mathematical problems, such as prime factorization, far more efficiently than classical computers. This capability could enable them to break widely used public-key cryptography algorithms, compromising sensitive data across various sectors. The "unbreakable" encryption developed by Lim Meng Liang and Ken Lin aims to circumvent this vulnerability. By building their system on the complex and often unsolvable nature of Diophantine equations, they posit that even the most powerful quantum computers would struggle to find the necessary solutions to decrypt the data. This forward-looking strategy has already attracted significant investment, with Aires having raised over US$2 million from private investors and government agencies, underscoring the growing industry focus on quantum-resistant cybersecurity solutions.

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How do Diophantine equations form the basis of this new encryption?

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