# Contributed Talks 5b

Fri, 6 Sep
, 11:20 - 13:10

- Quantum Key Leasing for PKE and FHE with a Classical LessorOrestis Chardouvelis (Carnegie Mellon University); Vipul Goyal (NTT Research, Carnegie Mellon University); Aayush Jain (Carnegie Mellon University); Jiahui Liu (Massachusetts Institute of Technology)[abstract]
**Abstract:**In this work, we consider the problem of secure key leasing, also known as revocable cryptography (Agarwal et. al. Eurocrypt' 23, Ananth et. al. TCC' 23), as a strengthened security notion to its predecessor put forward in Ananth et. al. (Eurocrypt' 21). This problem aims to leverage unclonable nature of quantum information to allow a lessor to lease a quantum key with reusability for evaluating a classical functionality. Later, the lessor can request the lessee to provably delete the key and then the lessee will be completely deprived of the capability to evaluate. In this work, we construct a secure key leasing scheme to lease a decryption key of a (classical) public-key, homomorphic encryption scheme from standard lattice assumptions. Our encryption scheme is exactly identical to the (primal) version of Gentry-Sahai-Waters homomorphic encryption scheme with a carefully chosen public key matrix. We achieve strong form of security where: The entire protocol (including key generation and verification of deletion) uses merely classical communication between a classical lessor (client) and a quantum lessee (server). Assuming standard assumptions, our security definition ensures that every computationally bounded quantum adversary could only simultaneously provide a valid classical deletion certificate and yet distinguish ciphertexts with at most some negligible probability. Our security relies on subexponential time hardness of learning with errors assumption. Our scheme is the first scheme to be based on a standard assumption and satisfying the two properties mentioned above. The main technical novelty in our work is the design of an FHE scheme that enables us to apply elegant analyses done in the context of classical verification of quantumness from LWE (Brakerski et. al.(FOCS'18, JACM'21) and its parallel amplified version in Radian et. al.(AFT'21)) to the setting of secure leasing. This connection to classical verification of quantumness leads to a modular construction and arguably simpler proofs than previously known. An important technical component we prove along the way is an amplified quantum search-to-decision reduction: we design an extractor that uses a quantum distinguisher (who has an internal quantum state) for decisional LWE, to extract secrets with success probability amplified to almost one. This technique might be of independent interest. - All graph state verification protocols are composably secureLéo Colisson (CWI/QuSoft, Amsterdam); Damian Markham (CNRS); Raja Yehia (ICFO)[abstract]
**Abstract:**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. - Quantum One-Wayness of the Single-Round Sponge with Invertible PermutationsJoseph Carolan (University of Maryland); Alexander Poremba (MIT)[abstract]
**Abstract:**Sponge hashing is a widely used class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a digest by once again iterating the block function on the final output bits. While much is known about the post-quantum security of the sponge construction in the case when the block function is modeled as a random function or one-way permutation, the case of permutations allowing inverse queries, which more accurately models the construction underlying SHA-3, has so far remained a fundamental open problem. In this work, we make new progress towards overcoming this barrier and show several results. First, we prove the “double-sided zero-search” conjecture proposed by Unruh (eprint’ 2021) and show that finding zero-pairs in a random 2n-bit permutation requires at least Ω(2^n/2) many queries—and this is tight due to Grover’s algorithm. At the core of our proof lies a novel “symmetrization argument” which uses insights from the theory of Young subgroups. Second, we consider more general variants of the double-sided search problem and show similar query lower bounds for them. As an application, we prove the quantum one-wayness of the single-round sponge with invertible permutations in the quantum random permutation model. - Succinct arguments for QMA from standard assumptions via compiled nonlocal gamesTony Metger (ETH Zurich); Anand Natarajan (MIT); Tina Zhang (MIT)[abstract]
**Abstract:**We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTO '22) also constructed a succinct classical argument system for QMA. However, their construction relied on post-quantumly secure indistinguishability obfuscation, a very strong primitive which is not known from standard cryptographic assumptions. In contrast, the primitives we use (namely, collapsing hash functions and a mild version of quantum homomorphic encryption) are much weaker and are implied by standard assumptions such as LWE. Our protocol is constructed using a general transformation which was designed by Kalai et al. (STOC '23) as a candidate method to compile any quantum nonlocal game into an argument system. Our main technical contribution is to analyze the soundness of this transformation when it is applied to a succinct self-test for Pauli measurements on maximally entangled states, the latter of which is a key component in the proof of MIP* = RE in quantum complexity. - Spanning tree packing algorithm for conference secret key propagation and GHZ distillationAnton Trushechkin (Heinrich Heine University Düsseldorf); Justus Neumann (Heinrich Heine University Düsseldorf); Hermann Kampermann (Heinrich Heine University Düsseldorf); Dagmar Bruss (Heinrich Heine University Düsseldorf)[abstract]
**Abstract:**Networks of nodes connected by pairwise quantum key distribution (QKD) links are actively developing now. We consider the following problem: Given pairwise secret keys from QKD, how to agree on a common (conference) key for the whole network using classical communication? We propose an algorithm based on spanning tree packing from the graph theory and prove its optimality. The same algorithm can be applied for the GHZ distillation in pair-entangled networks.