The concept of anamorphic encryption, first formally introduced by Persiano et al. in their influential 2022 paper titled ``Anamorphic Encryption: Private Communication Against a Dictator,'' enables embedding covert messages within ciphertexts. One of the key distinctions between a ciphertext embedding a covert message and an original ciphertext, compared to an anamorphic ciphertext, lies in the indistinguishability between the original ciphertext and the anamorphic ciphertext. This encryption procedure has been defined based on a public-key cryptosystem. Initially, we present a quantum analogue of the classical anamorphic encryption definition that is based on public-key encryption. Additionally, we introduce a definition of quantum anamorphic encryption that relies on symmetric key encryption. Furthermore, we provide a detailed generalized construction of quantum anamorphic symmetric key encryption within a general framework, which involves taking any two quantum density matrices of any different dimensions and constructing a single quantum density matrix, which is the quantum anamorphic ciphertext containing ciphertexts of both of them. Subsequently, we introduce a definition of computational anamorphic secret-sharing and extend the work of Çakan et al. on computational quantum secret-sharing to computational quantum anamorphic secret-sharing, specifically addressing scenarios with multiple messages, multiple keys, and a single share function. This proposed secret-sharing scheme demonstrates impeccable security measures against quantum adversaries.
The concept of anamorphic encryption, first formally introduced by Persiano et al. in their influential 2022 paper titled ``Anamorphic Encryption: Private Communication Against a Dictator,'' enables embedding covert messages within ciphertexts. One of the key distinctions between a ciphertext embedding a covert message and an original ciphertext, compared to an anamorphic ciphertext, lies in the indistinguishability between the original ciphertext and the anamorphic ciphertext. This encryption procedure has been defined based on a public-key cryptosystem. Initially, we present a quantum analogue of the classical anamorphic encryption definition that is based on public-key encryption. Additionally, we introduce a definition of quantum anamorphic encryption that relies on symmetric key encryption. Furthermore, we provide a detailed generalized construction of quantum anamorphic symmetric key encryption within a general framework, which involves taking any two quantum density matrices of any different dimensions and constructing a single quantum density matrix, which is the quantum anamorphic ciphertext containing ciphertexts of both of them. Subsequently, we introduce a definition of computational anamorphic secret-sharing and extend the work of Çakan et al. on computational quantum secret-sharing to computational quantum anamorphic secret-sharing, specifically addressing scenarios with multiple messages, multiple keys, and a single share function. This proposed secret-sharing scheme demonstrates impeccable security measures against quantum adversaries.
Anamorphic encryption is a cryptographic paradigm that allows covert messages to be hidden inside ordinary ciphertexts of a public-key encryption scheme. The covert channel is enabled by a secret double-key shared between the sender and an authorized receiver. Even if an adversary coerces the receiver into revealing the secret-key, the hidden communication remains undetectable without the double-key. Existing formulations of asymmetric anamorphic encryption suffer from two limitations. First, key pairs of a public-key encryption scheme and double-keys are tightly coupled: once a public-key is deployed, it is no longer possible to associate fresh double-keys with it. Second, existing constructions of asymmetric anamorphic encryption either rely on additional cryptographic primitives or on stronger structural assumptions, or they are scheme-specific.In this work, we refine the syntax of asymmetric anamorphic encryption so that double-key generation is separated from key deployment, allowing multiple double-keys to be registered with the same public-key after setup. We then construct an asymmetric anamorphic encryption scheme from the group-action-based public-key encryption scheme $ \mathsf{gaPKE} $, which is built from a regular effective group action over a commutative group. The resulting scheme is secure in the standard model. Our construction combines a hybrid encryption scheme, built under the $ \textsf{GA-DDH}$ assumption and entropy smoothing of hash functions, with a second independent group-action instance that carries the covert message. The resulting scheme satisfies anamorphic security, sender indistinguishability under chosen-plaintext attack security and colluder indistinguishability under chosen-plaintext attack security. We instantiate our framework in both post-quantum and classical settings. Using $ \textsf{CSIDH}$ group actions, we obtain the first isogeny-based asymmetric anamorphic encryption scheme. Using $ \textsf{DDH}$-hard groups, we obtain a classical anamorphic encryption scheme based on hashed ElGamal.
Anamorphic encryption serves as a vital tool for covert communication, maintaining secrecy even during post-compromise scenarios. Particularly in the receiver-anamorphic setting, a user can shield hidden messages even when coerced into surrendering their secret keys. However, a major bottleneck in existing research is the reliance on CPA-security, leaving the construction of a generic, CCA-secure anamorphic scheme in the standard model as a persistent open challenge. To bridge this gap, we formalize the Anamorphic Key Encapsulation Mechanism (AKEM), encompassing both Public-Key (PKAKEM) and Symmetric-Key (SKAKEM) variants. We propose generic constructions for these primitives, which can be instantiated using any KEM that facilitates randomness recovery. Notably, our framework achieves strong IND-CCA (sIND-CCA) security for the covert channel. We provide a rigorous formal proof in the standard model, demonstrating resilience against a "dictator" who controls the decapsulation key. The security of our approach is anchored in the injective property of the base KEM, which ensures a unique mapping between ciphertexts and randomness. By integrating anamorphism into the KEM-DEM paradigm, our work significantly enhances the practical utility of covert channels within modern cryptographic infrastructures.
We propose the concept ofQuantum Anamorphic Evolving Secret-Sharing(QAESS), combining two different cryptographic primitives in this paper. In QAESS, we have theanamorphic property, allowing alternate secrets to be embedded within the primary secret-sharing framework, accessible only under specific constraints, and theevolvingproperty ofsecret-sharing(ESS) where the scheme can dynamically adapt by accommodating potentially an infinite number of new parties without reinitialization. To achieve this, the major hurdles we encounter are 1) the large dimensions of shares and the requirement of huge quantum memory, and 2) the system breakdown by inserting a spy. In our first construction, we present a QAESS scheme, and in the second construction, we use secret redistribution to mitigate the above challenges. Our constructions extensively use quantum trap codes, random permutations, and data structure techniques. We analyze the schemes’ efficiency, scalability, and robustness through theoretical proofs and complexity estimates. This integration of quantum anamorphism and evolving properties finds potential application in several Internet of Things (IoT) and other practical scenarios. We close the paper by discussing several advantages of our constructions and some interesting problems for further study.
Privacy-preserving data-sharing mechanisms traditionally rely on data anonymization techniques, which aim to dissociate individual records from their corresponding data subjects in order to transform sensitive information into a form that minimizes the risk of re-identification. In parallel, trust-broker models have emerged as an additional layer of protection, whereby authorized data providers disclose controlled contact information that enables potential data users to request access under predefined conditions determined by the data owner. In contemporary data-sharing environments, cryptography remains a fundamental pillar for ensuring confidentiality and integrity during data exchange. Cryptographic protection typically involves two operations: an encryption process, in which the sender transforms plaintext into ciphertext that is unintelligible to unauthorized entities, and a decryption process, in which only the intended recipient restores the ciphertext to its original form. Both operations rely on a cryptographic algorithm paired with one or more secret keys. Symmetric-key cryptography employs a single shared key for both encryption and decryption. In contrast, asymmetric cryptography uses a mathematically linked pair of keys, where one key is used for encryption and the other for decryption. When the encryption key is publicly available while the corresponding decryption key remains private, only the legitimate recipient holding the private key is capable of recovering the plaintext. This cryptographic structure forms the basis for securing data confidentiality against unauthorized access in both classical and quantum-aware communication systems.
Anamorphic signatures allow covert communication through signatures in environments where encryption is restricted. They enable trusted recipients with a double-key to extract hidden messages while the signature remains indistinguishable from a regular one. However, the traditional notion of anamorphic signatures suffers from vulnerabilities, particularly when a single recipient or sender is compromised, exposing all hidden messages and providing undeniable proof that citizens are part of the anamorphic exchange. To address these limitations, we explore a threshold-based approach to distribute trust among multiple recipients, preventing adversaries from decrypting anamorphic messages even if some recipients are compromised. Our first contribution is the formalization of the notion of threshold-recipient anamorphic signatures, where decryption is possible only through collaboration among a subset of recipients. We then explore a stronger model in which the dictator controls the key-generation process through which it learns all secret keys, as well as how citizens store cryptographic keys. A particular example of this model in the real world is a dictator providing citizens with electronic identity documents (eIDs) and blocking all other usage of cryptography. We demonstrate that anamorphic communication is still possible even in such a scenario. Our construction is secure against quantum adversaries and does not rely on any computational assumptions beyond the random-oracle model. Finally, we present an impossibility result for encoding anamorphic messages with a threshold-sender model when using many existing threshold signature schemes, even when the adversary is part of the signing group. Our work outlines both the possibilities and limitations of extending anamorphic signatures with threshold cryptography, offering new insights into improving the security and privacy of individuals under authoritarian regimes.
Quantum image encryption has become a promising direction to protect visual information stored or transmitted through cyberspace due to its cryptographic power and resilience that are under-researched. This survey makes a systematic study of the current advancement in the field of quan-tum image encryption concerning cryptographic security and AI-based approaches. We survey the state of quantum-based encryption, such as quantum key distribution, chaotic quantum systems, and AI methods, such as deep learning, to generate keys and detect attacks through a thorough literature review. The significant findings include that quantum encryption may provide unprecedented security levels through mechanisms such as superposition and entanglement, yet computational complexity and hardware constraints are obstacles to implementation. AI-based methods have improved efficiency and adaptability but have created adversarial attack risks. We can conclude that quantum image encryption has the potential to transform the secure transmission of data, but it is necessary to incorporate AI-powered optimizations into the proven quantum systems to ensure scalability and resistance to evolving threats. Hybrid models are the way of the future as they need to find a balance between security and realistic usage.