Quantum Anamorphic Encryption and Secret-Sharing Enables Covert Message Embedding Within Ciphertexts

The secure transmission of information faces constant challenges, and researchers continually seek methods to conceal messages within seemingly normal communications, a concept explored through anamorphic encryption. Sayantan Ganguly and Shion Samadder Chaudhury, from the Institute for Advancing Intelligence, TCG CREST, and their colleagues, now advance this field by developing new forms of both anamorphic encryption and secret-sharing. Their work establishes a framework for embedding covert messages within ciphertexts in ways that are indistinguishable from standard encrypted data, extending the approach to both public and symmetric key systems. Crucially, the team also introduces a robust method for anamorphic secret-sharing, allowing multiple messages to be concealed and protected with a single share function, offering a significant step forward in secure communication technologies and data protection.

Quantum Key Distribution via State Shaping

This research introduces a novel approach to quantum key distribution inspired by classical optics, termed anamorphic encryption, where information is encoded by ‘shaping’ the quantum state of a carrier. Researchers are developing computational quantum anamorphic encryption, where security relies on the difficulty of decoding the anamorphic transformation, rather than relying on the fundamental laws of physics as in traditional quantum key distribution. The team has developed a framework for constructing anamorphic encryption schemes based on the computational difficulty of solving specific problems, and explores quantum anamorphic secret-sharing, a protocol allowing a secret to be divided among multiple parties such that no single party, or any combination of fewer than a threshold number, can reconstruct it. The proposed scheme leverages quantum entanglement and anamorphic transformations to encode the secret into a complex quantum state and distribute shares to the participating parties.

Reconstruction requires coordinated effort from at least a predetermined number of parties, each contributing their share to reveal the original secret. The team demonstrates that the proposed quantum anamorphic secret-sharing scheme is robust against various attacks, and security relies on the computational complexity of reversing the anamorphic transformation applied during encoding. This work introduces a new paradigm for quantum cryptography, offering a potentially more practical and scalable alternative to existing quantum key distribution protocols. Anamorphic encryption, formally introduced in 2022, enables the embedding of covert messages within ciphertexts, with a key distinction being the indistinguishability between the original and anamorphic ciphertexts. The team presents a quantum analogue of the classical anamorphic encryption definition, based on public-key encryption.

Fidelity Validates Quantum State Distinguishability

Scientists have rigorously proven that fidelity, a measure defined as the trace of the product of the square roots of two quantum states, is a valid measure of distinguishability. A valid measure must satisfy key properties, including symmetry, normalization, and a range between zero and one. Symmetry ensures that distinguishability between two states is independent of order, while normalization dictates that the distinguishability between a state and itself is maximal. The range between zero and one indicates the degree of distinguishability, with zero representing complete indistinguishability and one representing perfect distinguishability. The proof involves demonstrating that fidelity satisfies these properties through mathematical analysis and leveraging concepts from linear algebra and quantum mechanics, with the Cauchy-Schwarz inequality playing a crucial role. This rigorous validation confirms that fidelity is a reliable and widely used measure for quantifying the distinguishability between quantum states, providing a fundamental tool for understanding and manipulating quantum information.

Anamorphic Encryption and Secret Sharing Schemes

This research significantly advances the field of cryptographic encryption by formally exploring and extending the concept of anamorphic encryption. Scientists have developed definitions for anamorphic encryption based on both public and symmetric key systems, providing a generalized framework for constructing symmetric key anamorphic encryption from diverse density matrices, and allowing for the embedding of covert messages within ciphertexts. Furthermore, the team extended existing computational secret-sharing techniques to create a computational anamorphic secret-sharing scheme, successfully addressing scenarios involving multiple messages, keys, and a single share function, and demonstrating robust security against potential adversaries. The authors acknowledge that the practicality of these schemes depends on qubit requirements and entropy computations, areas requiring further investigation, with future work likely focusing on optimising these computational aspects and exploring resilience against more sophisticated attacks.