On the Impossibility of Key Agreements from Quantum Random Oracles
We study the following question, ﬁrst publicly posed by Hosoyamada and Yamakawa in 2018. Can parties A, B with local quantum computing power rely (only) on a random oracle and classical communication to agree on a key? (Note that A, B can now query the random oracle at quantum superpositions.) We make the ﬁrst progress on the question above and prove the following. – When only one of the parties A is classical and the other party B is quantum powered, as long as they ask a total of d oracle queries and agree on a key with probability 1, then there is always a way to break the key agreement by asking O(d^2) number of classical oracle queries. – When both parties can make quantum queries to the random oracle, we introduce a natural conjecture, which if true would imply attacks with poly(d) classical queries to the random oracle. Our conjecture, roughly speaking, states that the multiplication of any two degree-d real-valued polynomials over the Boolean hypercube of inﬂuence at most δ = 1/ poly(d) is nonzero. We then prove our conjecture for exponentially small inﬂuences, which leads to an (unconditional) classical 2^O(md)-query attack on any such key agreement protocol, where m is the random oracle’s output length. – Since our attacks are classical, we then ask whether it is possible to ﬁnd such classical attacks in general. We prove a barrier for this approach, by showing that if the folklore “simulation conjecture” about the possibility of simulating efﬁcient-query quantum algorithms classically is false, then that implies a possible quantum protocol that cannot be broken by classical adversaries.
Round Efficient Secure Multiparty Quantum Computation with Identifiable Abort 📺
A recent result by Dulek et al. (EUROCRYPT 2020) showed a secure protocol for computing any quantum circuit even without the presence of an honest majority. Their protocol, however, is susceptible to a ``denial of service'' attack and allows even a single corrupted party to force an abort. We propose the first quantum protocol that admits security-with-identifiable-abort, which allows the honest parties to agree on the identity of a corrupted party in case of an abort. Additionally, our protocol is the first to have the property that the number of rounds where quantum communication is required is independent of the circuit complexity. Furthermore, if there exists a post-quantum secure classical protocol whose round complexity is independent of the circuit complexity, then our protocol has this property as well. Our protocol is secure under the assumption that classical quantum-resistant fully homomorphic encryption schemes with decryption circuit of logarithmic depth exist. Interestingly, our construction also admits a reduction from quantum fair secure computation to classical fair secure computation.