Léo Colisson

Graph state verification protocols allow multiple parties to share a graph state while checking that the state is honestly prepared, even in the presence of malicious parties. Since graph states are the starting point of numerous quantum protocols, it is crucial to ensure that graph state verification protocols can safely be composed with other protocols, this property being known as composable security. Previous works conjectured that such a property could not be proven within the abstract cryptography framework: we disprove this conjecture by showing that all graph state verification protocols can be turned into a composably secure protocol with respect to the natural functionality for graph state preparation. Moreover, we show that any unchanged graph state verification protocol can also be considered as composably secure for a slightly different, yet useful, functionality. Finally, we show that these two results are optimal, in the sense that any such generic result, considering arbitrary black-box protocols, must either modify the protocol or consider a different functionality. Along the way, we show a protocol to generalize entanglement swapping to arbitrary graph states that might be of independent interest.

We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable (quantum) oblivious transfer (OT) protocol, mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions…) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely to exist classically as Cryptomania is believed to be different from Minicrypt. In particular, by instantiating our construction using Non-Interactive ZK (NIZK), we provide the first round-optimal (2-message) quantum OT protocol secure in the random oracle model, and round-optimal extensions to string and k-out-of-n OT. At the heart of our construction lies a new method that allows us to prove properties on a received quantum state without revealing additional information on it, even in a non-interactive way and/or with statistical guarantees when using an appropriate classical ZK protocol. We can notably prove that a state has been partially measured (with arbitrary constraints on the set of measured qubits), without revealing any additional information on this set. This notion can be seen as an analog of ZK to quantum states, and we expect it to be of independent interest as it extends complexity theory to quantum languages, as illustrated by the two new complexity classes we introduce, ZKstatesQIP and ZKstatesQMA.

Classical remote state preparation (RSPCC) is a primitive that allows an honest client to prepare a quantum state remotely with the help of an (untrustworthy) server using only a classical communication channel. With this primitive quantum protocols (such as secure delegation of quantum computations) become accessible to classical clients, by removing the need for a quantum channel. Since this cryptographic primitive’s main role is to be a building block within larger protocols, it is of utmost importance to examine its security under composition. In this work we present three results related to the composability of RSPCC protocols: 1. As our first main result, we show that no classical remote state preparation protocol RSPCC can be composable in the Abstract Cryptography framework [MR11], even when the distinguisher is computationally bounded. In other words, remote state preparation cannot be constructed with only a classical channel. 2. We further show that any classical-client delegated quantum computing protocol that uses the universal blind quantum computation (UBQC) protocol [BFK09] and a RSPCC protocol as a subroutine cannot be composable. 3. Upon relaxing the security requirement, we show that replacing the quantum channel of the UBQC protocol by the particular RSPCC protocol of [CCKW19] is secure in the game-based security framework.