In this note, we consider the setting of uncloneable encryption satisfying uncloneable indistinguishability, a form of symmetric key encryption that prevents the cloning of ciphertexts in a very strong sense. Our goal is to minimize the assumptions under which (many-time secure) uncloneable encryption is known to exist, assuming the existence of an information-theoretic "uncloneable bit", i.e. a one-time secure uncloneable encryption scheme for one-bit messages. We observe that if a t -> t' uncloneable bit exists, then the following implications hold.
1. If many-time secure symmetric key encryption exists, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages exists. Since many-time secure uncloneable encryption implies many-time secure symmetric key encryption, this result is tight.
2. If pseudorandom unitaries exist, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages with identical copy security exists.
These results together show that many-time secure uncloneable encryption may follow from concrete assumptions in "microcrypt", the world of unstructured quantum cryptography that plausibly exists even if P = NP.
In this note, we consider the setting of uncloneable encryption satisfying uncloneable indistinguishability, a form of symmetric key encryption that prevents the cloning of ciphertexts in a very strong sense. Our goal is to minimize the assumptions under which (many-time secure) uncloneable encryption is known to exist, assuming the existence of an information-theoretic "uncloneable bit", i.e. a one-time secure uncloneable encryption scheme for one-bit messages. We observe that if a t -> t' uncloneable bit exists, then the following implications hold.
If many-time secure symmetric key encryption exists, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages exists. Since many-time secure uncloneable encryption implies many-time secure symmetric key encryption, this result is tight.
If pseudorandom unitaries exist, then many-time secure t -> t' uncloneable encryption for arbitrary-length messages with identical copy security exists.
These results together show that many-time secure uncloneable encryption may follow from concrete assumptions in "microcrypt", the world of unstructured quantum cryptography that plausibly exists even if P = NP.
We construct unclonable encryption (UE) in the Haar random oracle model, where all parties have query access to U,U†,U∗,UT for a Haar random unitary U. Our scheme satisfies the standard notion of unclonable indistinguishability security, supports reuse of the secret key, and can encrypt arbitrary-length messages. That is, we give the first evidence that (reusable) UE, which requires computational assumptions, exists in "microcrypt", a world where one-way functions may not exist.
As one of our central technical contributions, we build on the recently introduced path recording framework to prove a natural ``unitary reprogramming lemma'', which may be of independent interest.
Unconditional uncloneable encryption of a single bit with efficient encryption and decryption is now possible. However, whether the extension to messages of arbitrary length achieves statistical security remains to be known. Using the fact that the encoding bases for the single-bit scheme known to be secure consist of a subset of the Clifford unitaries, we show that this scheme can be upgraded to achieve unconditional uncloneable encryption for messages of arbitrary length, with encoding time polynomial in the message length and security parameter. This establishes that one-time uncloneable encryption of arbitrary messages enjoys statistical security.
We give an unconditional construction of information-theoretically secure one-time private-key unclonable encryption for one-bit messages, with efficient encryption and decryption and exponentially small unclonable-indistinguishability advantage. Previous work by Bhattacharyya and Culf (Nature Physics, 2026) and Bhattacharyya, Broadbent, and Culf (arXiv:2603.08916) either only showed inverse-polynomial security loss or required inefficient encryption/decryption operations; we avoid both of these caveats.
Our scheme's key is a uniformly random non-identity phase-free Pauli on n qubits, and bit a is encrypted as a random (−1)a eigenstate of that Pauli. We prove that the probability that both receivers recover the bit is at most 1/2+O(2−n/2). By a lower bound due to Broadbent, Culf, and Rochette (arXiv:2510.00903), this is the best probability bound achievable with n-qubit ciphertexts while ensuring perfect correctness (up to the constant hidden in the O(⋅)).
We give, to our knowledge, the first plain-model, one-time information-theoretically secure, efficient unclonable encryption scheme for one classical bit. Previous work by Bhattacharyya and Culf (Nature Physics, 2026) and Bhattacharyya, Broadbent, and Culf either only showed 1/poly(λ) security loss or required inefficient encryption/decryption operations. We avoid both of these caveats; in doing so, we obtain (to our knowledge) the first plain-model construction of many-time secure 1→2 unclonable encryption for arbitrary polynomial-length messages, assuming the existence of pseudorandom function-like states (Bartusek and Goldin).
The key is a uniformly random non-identity phase-free Pauli on n qubits, and bit a is encrypted as a random (−1)a eigenstate of that Pauli. The scheme is exponentially secure; we prove that the probability that both receivers recover the bit is at most 21+212n/(4n−1)=21+O(2−n/2). By a lower bound due to Broadbent, Culf, and Rochette, this is the best probability bound achievable with n-qubit ciphertexts (up to the constant hidden in the O(⋅)).
The main conceptual idea is to leverage, in a precise spectral sense, the balanced commutation-anticommutation structure of the Pauli group. The proof is intricate but completely elementary and makes use of standard spectral bound techniques. The main technical workhorse is a standalone linear-algebraic lemma that informally relates the positivity of two different operators, each capturing the intuition that if the two receivers can individually decrypt unusually often then they must also disagree often.
GPT-5.6 Sol Ultra found this proof in an extended conversation with the author and drafted a preliminary version of this paper. The author is fully accountable for the correctness of this paper.
We establish quantum uncloneable encryption with unconditional security, preventing two non-communicating adversaries from simultaneously decrypting a single ciphertext − even when both are given the key. Our construction achieves security that approaches the ideal limit at a rate that is exponentially small in the security parameter, without employing any assumptions. Our proof invokes unitary invariance of the shared entangled state and simplifies the adversarial strategies by enforcing this symmetry. Crucially, it then rules out the sender being highly correlated with two non-communicating adversaries at once by an approximation property that we develop, for such unitarily invariant states, which yields a near-optimal bound on the probability of cloning. Consequently, no coordinated strategy beats random guessing of the encrypted bit, establishing unconditional uncloneability. This reveals the existence of an uncloneable bit in Nature and delineates a fundamental, physically enforced cryptographic primitive unavailable in classical settings.
We study uncloneable quantum encryption schemes for classical messages as recently proposed by Broadbent and Lord. We focus on the information-theoretic setting and give several limitations on the structure and security of these schemes: Concretely, 1) We give an explicit cloning-indistinguishable attack that succeeds with probability 21+μ/16 where μ is related to the largest eigenvalue of the resulting quantum ciphertexts. 2) For a uniform message distribution, we partially characterize the scheme with the minimal success probability for cloning attacks. 3) Under natural symmetry conditions, we prove that the rank of the ciphertext density operators has to grow at least logarithmically in the number of messages to ensure uncloneable security. 4) The \emph{simultaneous} one-way-to-hiding (O2H) lemma is an important technique in recent works on uncloneable encryption and quantum copy protection. We give an explicit example which shatters the hope of reducing the multiplicative "security loss" constant in this lemma to below 9/8.