Frédéric Dupuis

We explore the cryptographic power of arbitrary shared physical resources. The most general such resource is access to a fresh entangled quantum state at the outset of each protocol execution. We call this the Common Reference Quantum State (CRQS) model, in analogy to the well-known Common Reference String (CRS). The CRQS model is a natural generalization of the CRS model but appears to be more powerful: in the two-party setting, a CRQS can sometimes exhibit properties associated with a Random Oracle queried once by measuring a maximally entangled state in one of many mutually unbiased bases. We formalize this notion as a Weak One-Time Random Oracle (WOTRO), where we only ask of the m–bit output to have some randomness when conditioned on the n–bit input. We show that when n − m ∈ ω(lg n), any protocol for WOTRO in the CRQS model can be attacked by an (inefficient) adversary. Moreover, our adversary is efficiently simulatable, which rules out the possibility of proving the computational security of a scheme by a fully black-box reduction to a cryptographic game assumption. On the other hand, we introduce a non-game quantum assumption for hash functions that implies WOTRO in the CRQ$ model (where the CRQS consists only of EPR pairs). We first build a statistically secure WOTRO protocol where m = n, then hash the output. The impossibility of WOTRO has the following consequences. First, we show the fully-black-box impossibility of a quantum Fiat-Shamir transform, extending the impossibility result of Bitansky et al. (TCC ’13) to the CRQS model. Second, we show a fully-black-box impossibility result for a strenghtened version of quantum lightning (Zhandry, Eurocrypt ’19) where quantum bolts have an additional parameter that cannot be changed without generating new bolts. Our results also apply to 2–message protocols in the plain model.

We prove an achievability result for privacy amplification and decoupling in terms of the sandwiched Rényi entropy of order α ∈ (1,2]; this extends previous results which worked for α=2. The fact that this proof works for α close to 1 means that we can bypass the smooth min-entropy in the many applications where the bound comes from the fully quantum AEP or entropy accumulation (EAT), and carry out the whole proof using the Rényi entropy, thereby easily obtaining an error exponent for the final task. This effectively replaces smoothing, which is a difficult high-dimensional optimization problem, by an optimization problem over a single real parameter α. This can be applied directly to QKD security proofs---including device independent protocols---by combining it with the entropy accumulation theorem.

One of the most basic and intuitive properties of most information measures is that the amount of information carried by a physical system must be bounded by its size. We consider locking, which occurs when classical information encoded into a quantum system can be extracted given access to the cyphertext only with much less probability than expected. We show that locking occurs with high probability in physical systems whose internal dynamics are sufficiently random, with implications for thermodynamics and the black hole information problem. We also generalise locking to the case where the measuring device is allowed to share entanglement with the cyphertext-key compound system.