Computational Quantum Anamorphic Encryption and Quantum Anamorphic Secret-Sharing
Sayantan Ganguly, Shion Samadder Chaudhury
TL;DR
This work extends anamorphic encryption to the quantum realm by defining quantum analogues of anamorphic public-key and symmetric-key encryption, and by constructing a general quantum anamorphic symmetric-key scheme that hides a covert quantum message inside a normal ciphertext. It establishes qIND-qCPA security via two-world indistinguishability games and provides a detailed main construction using dual QOTP encryptions, density-matrix padding, and Halmos-based off-diagonal embeddings, with rigorous correctness and finite-data analysis. Beyond encryption, the paper develops quantum anamorphic secret-sharing, including a compiler that combines classical secret-sharing with quantum error-correcting codes to realize no-cloning monotone functions and to embed covert shares within the secret-sharing framework. The results demonstrate perfect or computational privacy against quantum adversaries and pave the way for covert quantum communications and secret-sharing capabilities, with concrete analyses of qubit requirements and entropy changes relevant to implementation.
Abstract
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.