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Singularity Cipher: A Topology-Driven Cryptographic Scheme Based on Visual Paradox and Klein Bottle Illusions
Perspective | Published: 19 August 2025
ICCK Transactions on Information Security and Cryptography Volume 1, Issue 1, 2025: 38-53
Volume 1, Issue 1, ICCK Transactions on Information Security and Cryptography
Volume 1, Issue 1, 2025
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Donghua Jiang
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ICCK Transactions on Information Security and Cryptography, Volume 1, Issue 1, 2025: 38-53

Open Access | Perspective | 19 August 2025
Singularity Cipher: A Topology-Driven Cryptographic Scheme Based on Visual Paradox and Klein Bottle Illusions
by
Abraham Itzhak Weinberg Abraham Itzhak Weinberg 1 *
1 AI-WEINBERG, AI Experts, Tel-Aviv, Israel
* Corresponding Author: Abraham Itzhak Weinberg, [email protected]
DOI: 10.62762/TISC.2025.186894
Received: 08 July 2025, Accepted: 31 July 2025, Published: 19 August 2025  
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Abstract
This paper presents the Singularity Cipher, a novel cryptographic-steganographic framework that integrates topological transformations and visual paradoxes to achieve multidimensional security. Inspired by the non-orientable properties of the Klein bottle—constructed from two Möbius strips—the cipher applies symbolic twist functions to simulate topological traversal, producing high confusion and diffusion in the ciphertext. The resulting binary data is then encoded using perceptual illusions, such as the missing square paradox, to visually obscure the presence of encrypted content. Unlike conventional ciphers that rely solely on algebraic complexity, the Singularity Cipher introduces a dual-layer approach: symbolic encryption rooted in topology and visual steganography designed for human cognitive ambiguity. This combination enhances both cryptographic strength and detection resistance, making it well-suited for secure communication, watermarking, and plausible deniability in adversarial environments. The paper formalizes the architecture, provides encryption and decryption algorithms, evaluates security properties, and compares the method against classical, post-quantum, and steganographic approaches. Potential applications and future research directions are also discussed.
Graphical Abstract
Singularity Cipher: A Topology-Driven Cryptographic Scheme Based on Visual Paradox and Klein Bottle Illusions
Keywords
topological cryptography
visual steganography
klein bottle cipher
post-quantum security
cognitive encryption
Data Availability Statement
Data will be made available on request.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
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Cite This Article
APA Style
Weinberg, A. I. (2025). Singularity Cipher: A Topology-Driven Cryptographic Scheme Based on Visual Paradox and Klein Bottle Illusions. ICCK Transactions on Information Security and Cryptography, 1(1), 38–53. https://doi.org/10.62762/TISC.2025.186894
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