Quandle Encryption Using Binary Operations for Quantum Resistance
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Solution Overview
Problem
Conventional encryption techniques, such as RSA, DH, and ECDH, are vulnerable to quantum computing attacks due to the efficiency of quantum algorithms in solving underlying mathematical problems, compromising cryptographic security.
Innovation Solution
A secure encryption technique based on quandle algebra, utilizing binary operations that satisfy quandle axioms, including the use of rational numbers and multiple encoding variables, to generate and decrypt ciphertexts, ensuring complex data manipulations while maintaining message integrity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional encryption techniques (RSA, DH, ECDH) are used, then cryptographic security is maintained against classical attacks, but security is compromised against quantum computing attacks
Solution Approach 1:
The patent changes the mathematical foundation of encryption from number-theoretic problems (factorization, discrete logarithm) to knot theory-based invariants. This parameter change in the underlying mathematical structure makes the encryption resistant to quantum algorithms like Shor's algorithm while maintaining security properties.
Solution Approach 2:
The patent replaces the traditional algebraic-mechanical cryptographic systems (RSA, DH, ECDH) with a topological system based on knot theory. This substitution uses fundamentally different mathematical principles (topological invariants vs. number theory) that are not vulnerable to quantum computational attacks.
2Reliability
If quandle-based encryption is implemented, then security against quantum attacks is enhanced, but computational complexity increases
Solution Approach 1:
The patent segments the encryption process into distinct operations: creating knot structures from messages, computing topological invariants (like Jones polynomials), and applying quandle operations. This segmentation allows for systematic implementation and optimization of each component separately.
Solution Approach 2:
The patent introduces topological invariants (such as Jones polynomials) as intermediaries between the plaintext message and the ciphertext. These invariants serve as mathematical mediators that transform the message into a form that is both secure against quantum attacks and computationally manageable.
3Manufacturing precision
If multiple encoding variables are used in quandle-based encryption, then message integrity is maintained, but encryption process complexity increases
Solution Approach 1:
The patent applies preliminary actions by first transforming the message into a knot structure, then computing its topological invariants before applying the quandle encryption operation. This preliminary processing ensures that the essential characteristics of the message are preserved and can be verified during decryption.
Solution Approach 2:
The patent incorporates feedback mechanisms where the topological invariants of the original message are computed and used to verify the correctness of the decryption process. This feedback ensures message integrity by confirming that the decrypted message has the same topological properties as the original.
Data Source
AI summary
Systems and methods are described for secure communication to facilitate encrypted transmission of data between a transmitting device (encoder) and a receiving device (decoder), leveraging quandle algebra. An example system includes an encoder, a decoder, and a communication channel. The encoder may generate a ciphertext (c) based on a message (x), an encoding variable (y), and a public encryption key (e), wherein, c = x ▷ y. The cipher text (c) is then transmitted, via the communication channel, to the decoder. The decoder may receive the ciphertext (c) via the communication channel and generate a deciphered form (x') of the message (x) based on the ciphertext (c), the encoding variable (y), and a private encryption key (f), wherein, x' = c ◁ y, and ▷ and ◁ are binary operations that satisfy axioms of a quandle and/or a rack.