Quantum information enables many cryptographic primitives that are impossible in the classical world. A line of works has developed cryptographic protocol under the assumption that quantum adversaries are restricted to noisy intermediate-scale quantum (NISQ) computing power, enabling strong one-time functionalities. But the advent of early fault-tolerant quantum computers eras will allow deeper logical quantum circuits, calling into questions the applicability of these NISQ-based assumptions.
In this work, we adapt the classically accessible random oracle model (CAROM) as in [BDF+11] and [AK22], in which adversaries are only allowed to classically query the random oracle. The restriction is well motivated for NISQ quantum adversaries and may remain plausible in the presence of early fault-tolerant quantum computers. Then, we show that an efficient simulation-secure one-time memory (OTM) is possible under CAROM. Our protocol uses only BB84 states and has quadratic communication: for a $λ$-bit message and integer-valued parameters $n=n(λ)$ and $\ell=\ell(λ)$, the construction uses $n\ell$ qubits and $(n+2)λ$ classical bits, and for any quantum adversary with at most $2^{\ell/2-1}-1$ classical queries to the random oracle, its simulation advantage is at most $(n+3)\left(\frac{3}{4}\right)^n.$ Hence exponentially small simulation advantage in $n$.
Quantum information enables many cryptographic primitives that are impossible in the classical world. A line of works has developed cryptographic protocol under the assumption that quantum adversaries are restricted to noisy intermediate-scale quantum (NISQ) computing power, enabling strong one-time functionalities. But the advent of early fault-tolerant quantum computers eras will allow deeper logical quantum circuits, calling into questions the applicability of these NISQ-based assumptions.
In this work, we adapt the classically accessible random oracle model (CAROM) as in [BDF+11] and [AK22], in which adversaries are only allowed to classically query the random oracle. The restriction is well motivated for NISQ quantum adversaries and may remain plausible in the presence of early fault-tolerant quantum computers. Then, we show that an efficient simulation-secure one-time memory (OTM) is possible under CAROM. Our protocol uses only BB84 states and has quadratic communication: for a λ-bit message and integer-valued parameters n=n(λ) and ℓ=ℓ(λ), the construction uses nℓ qubits and (n+2)λ classical bits, and for any quantum adversary with at most 2ℓ/2−1−1 classical queries to the random oracle, its simulation advantage is at most (n+3)(43)n. Hence exponentially small simulation advantage in n.
We construct simulation-secure one-time memories (OTM) in the random oracle model, and present a plausible argument for their security against quantum adversaries with bounded and adaptive depth. Our contributions include: (1) A simple scheme where we use only single-qubit Wiesner states and conjunction obfuscation (constructible from LPN): no complex entanglement or quantum cryptography is required. (2) A new POVM bound where e prove that any measurement achieving (1−ε) success on one basis has conjugate-basis guessing probability at most 2m1+O(ε41). (3) Simultation-secure OTMs in the quantum random oracle model where an adversary can only query the random oracle classically. (4) Adaptive depth security where, via an informal application of a lifting theorem from Arora et al., we conjecture security against adversaries with polynomial quantum circuit depth between random oracle queries.
Security against adaptive, depth-bounded, quantum adversaries captures many realistic attacks on OTMs built from single-qubit states; our work thus paves the way for practical and truly secure one-time programs. Moreover, depth bounded adaptive adversarial models may allow for encoding one-time memories into error corrected memory states, opening the door to implementations of one-time programs which persist for long periods of time.
With the power of quantum information, we can achieve exciting and classically impossible cryptographic primitives. However, almost all quantum cryptography faces extreme difficulties with the near-term intermediate-scale quantum technology (NISQ technology); namely, the short lifespan of quantum states and limited sequential computation. At the same time, considering only limited quantum adversaries may still enable us to achieve never-before-possible tasks. In this work, we consider quantum cryptographic primitives against limited quantum adversaries - depth-bounded adversaries. We introduce a model for (depth-bounded) NISQ computers, which are classical circuits interleaved with shallow quantum circuits. Then, we show one-time memory can be achieved against any depth-bounded quantum adversaries introduced in the work, with their depth being any pre-fixed polynomial. Therefore we obtain applications like one-time programs and one-time proofs. Finally, we show our one-time memory has correctness even against constant-rate errors.
We construct a quantum public key encryption scheme from oneway functions in the random oracle model. While our construction only has indistinguishability against restricted adversaries, who perform individual attacks and can only make classical queries to the random oracle, it possesses two practical advantages that were not achieved in previous works. First, legitimate participants can discard noisy quantum public keys. Second, the scheme only requires products of single-qubit states, and it does not require quantum computing or quantum memory for legitimate participants. Although the security does not hold against adversaries capable of large-scale quantum computation, we believe that our protocol is well-suited for the near-term stage of the quantum era.
Publicly accessible fault-tolerant quantum computers must preserve scientific utility while limiting cryptanalytic power. We propose the restricted model of computation, 1/2BQP_1: a quantum server provides random computational-basis inputs, revealed only after execution, and one designated output bit. This interface permits arbitrary circuits and system sizes. We conjecture that a classical client making polynomially many adaptive requests cannot efficiently factor RSA moduli. The model subsumes the well-known one-clean-qubit model DQC1, retaining its applications to infinite-temperature multi-time correlations, out-of-time-order correlators, and suitably normalized partition functions. We propose a candidate for separating 1/2BQP_1 from DQC1 based on testing classical predictions of quantum spin dynamics. We argue security in two steps. First, we show that one-bit readout makes the quantum stages of standard factoring algorithms classically simulable, even when their preparation and postprocessing are redesigned within a broad family around a single arithmetic-oracle call. This covers the quantum stages of Shor, Ekera-Hastad, Kitaev, and Regev factoring constructions. Second, we examine the workaround of coherently implementing rational reconstruction to release a factor bit. Random inputs obstruct this straightforward attack: known techniques accommodate logarithmic-depth classical circuits, but rational reconstruction has resisted such parallelization for decades. Therefore, we show that security of our protocol is built on not only classical hardness for factoring, but also conjectured circuit lowerbounds for rational reconstruction.
A central tenet of theoretical cryptography is the study of the minimal assumptions required to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we propose a scheme for using quantum information, together with the assumption of stateless ( i.e. , reusable) hardware tokens, to build statistically secure OTMs. Via the semidefinite programming-based quantum games framework of Gutoski and Watrous [STOC 2007], we prove security for a malicious receiver making at most 0.114 n adaptive queries to the token (for n the key size), in the quantum universal composability framework, but leave open the question of security against a polynomial amount of queries. Compared to alternative schemes derived from the literature on quantum money, our scheme is technologically simple since it is of the "prepare-and-measure" type. We also give two impossibility results showing certain assumptions in our scheme cannot be relaxed.
We prove near-optimal lower bounds for preprocessing attacks on quantum cryptography in the random oracle model. Specifically, we show that a T-query adversary with S qubits of non-uniform advice can recover a random key k from the n-qubit binary phase state ∣ψk⟩∝∑xR(k,x)∣x⟩ with probability at most O(NT2+ST) for N=2n. In contrast, the best known bound for post-quantum one-way functions is O(NT2+ST), with a trivial attack at S=N. This demonstrates a new advantage of quantum cryptography over classical cryptography: n qubits of communication suffice for security against preprocessing attacks with space up to N2 rather than N. Our methodology is simple: express the optimal preprocessing attack as the operator norm of a random matrix, and bound this value in expectation over the random oracle via the trace-moment method. These trace moments have a natural interpretation using compressed oracles [Zhandry, Crypto 2019], which we then analyze. This can be viewed as a simplification and generalization of the approach of Liu [Eurocrypt 2023] for proving the security of post-quantum cryptography against preprocessing attacks. We also prove the following results: (1) We tighten Liu's analysis of post-quantum PRGs in QROM, achieving a distinguishing advantage bound of O(NT2+NST). (2) For unitary synthesis, we extend the one-query lower bound of Lombardi-Ma-Wright [STOC 2024] to hold against adversaries that can make one arbitrary function query along with polynomially many (adaptive) queries to the random oracle, either before or after the function query. This also interprets the original LMW24 result in terms of compressed oracles. (3) Finally, we prove a tight O(NS) bound for the pseudorandomness of random binary phase states against space S distinguishers.