Applications of the proposed primitive: Quantum Primitive for Output-Hiding Function Sharing, are discussed for secure quantum communications and computation protocols. In particular, QKD applications provide notable enhanced security and efficiency properties relative to status-quo protocols. Additionally, we provide examples when parties may wish to encode joint functions, or decisions, which remain information-theoretically hidden from external parties and those internal to the quantum system, without additional private keys, hidden randomness, or classical communication. In particular these applications may be useful in domains such as; financial transactions, joint signaling or coordination decisions, and navigation systems, among others.
A quantum information-theoretic primitive is introduced for determining a discrete-valued function that depends on multiple parties' local private inputs. The primitive permits the parties to mutually learn each others' local inputs, and thereby determine function values, while their individual systems remain independent of these inputs. The resulting function values are shared among the parties, but may remain information-theoretically hidden from any external observer, as well as from adversarial state-preparation or measurement processes within the quantum system, in every iteration. In particular, while classically producing a shared function with these information-theoretic properties requires the use of private keys or hidden randomness, in the proposed setting it is achieved using quantum resources alone. I outline the primitive's general properties while applications across a broad range of secure quantum communication and computation settings including: quantum key distribution, multi-party coordination and decision schemes, function evaluation, and in some settings, protocols for fairly generated private coins, are relegated to further publications.
Nowadays the need of securely transmitting information has become crucial due to the increasing threat of cyberattacks. Quantum Key Distribution (QKD) guarantees information-theoretic security in the transmission of secure keys between two trusted parties, leveraging the laws of quantum mechanics. In more general mistrustful communication scenarios, alternative protocols, often referred to as beyond-QKD protocols, are employed [1]. A notable example is oblivious transfer, a cryptographic primitive that supports secure multiparty computation (SMC).
How could quantum cryptography help us achieve what are not achievable in classical cryptography? In this work we study the classical cryptographic problem that two parties would like to perform secure computations with long outputs. As a basic primitive and example, we first consider the following problem which we call secure function sampling with long outputs: suppose
f:{0,1}n→{0,1}m is a public, efficient classical function, where
m is big; Alice would like to sample
x from its domain and sends
f(x) to Bob; what Bob knows should be no more than
f(x) even if it behaves maliciously. Classical cryptography, like FHE and succinct arguments [Gen09,Kil92,HW15], allows us to achieve this task within communication complexity
O(n+m); could we achieve this task with communication complexity independent of
m? In this work, we first design a quantum cryptographic protocol that achieves secure function sampling with approximate security, within
O(n) communication (omitting the dependency on the security parameter and error tolerance). We also prove the classical impossibility using techniques in [HW15], which means that our protocol indeed achieves a type of quantum advantage. Building on the secure function sampling protocol, we further construct protocols for general secure two-party computations [Yao86,GB01] with approximate security, with communication complexity only depending on the input length and the targeted security. In terms of the assumptions, we construct protocols for these problems assuming only the existence of collapsing hash functions [Unr16]; what's more, we also construct a classical-channel protocol for these problems additionally assuming the existence of noisy trapdoor claw-free functions [BCMVV,BKVV].
We present protocols for multiparty data hiding of quantum information that implement all possible threshold access structures. Closely related to secret sharing, data hiding has a more demanding security requirement: that the data remain secure against unrestricted attacks via local operation and classical communication. In the limit of hiding a large amount of data, our protocols achieve an asymptotic rate of one hidden qubit per local physical qubit. That is, each party holds a share that is the same size as the hidden state to leading order, with accuracy and security parameters incurring an overhead that is asymptotically negligible. The data-hiding states have very unusual entanglement properties, which we briefly discuss.
Quantum cryptographic primitives beyond key distribution remain a less well understood area of research. In classical cryptography, one-way functions underpin nearly all standard cryptographic protocols, motivating the search for meaningful quantum analogues and for a clear understanding of the physical and computational mechanisms that could enforce one-wayness. In this article, we review quantum one-way functions and a range of closely related quantum-state primitives, including one-way state generators, pseudorandom quantum states, and efficiently indistinguishable pairs of states. We discuss both computational and information-theoretic notions of quantum one-wayness, emphasizing the different adversarial models and security assumptions that underlie these constructions. We compare and contrast the various proposed primitives, and clarify their conceptual relationships. Particular emphasis is placed on questions of physical realizability, experimental feasibility, and robustness to noise. Finally, we outline open problems and future directions toward the development of practical quantum cryptographic primitives beyond key distribution, and the emergence of a broader quantum-cryptographic ecosystem.
Secure multi-party computation (MPC) is a cryptographic primitive that lets a num- ber N of mutually distrustful parties compute a function f (x1, . . . , xN ) on their private inputs xi such that at the end of the MPC protocol, each honest party obtains the func- tion’s correct output and no adversary controlling a certain subset of parties learns any- thing about the honest parties’ inputs beyond what can be inferred from the function’s output value. In 2002, [Smi01] and [CGS02] introduced the notion of multi-party quan- tum computation (MPQC) in which arbitrary quantum circuits can be evaluated in a distributed manner, secure against a quantum adversary. Few protocols for MPQC are known. We present a fundamental study of the building blocks of MPC and MPQC in the information-theoretic setting with a focus on protocols built on top of (quantum) se- cret sharing schemes. In particular, we point out structural similarities and differences and compile an extensive list of theoretical feasibility results for the maximum number of corrupted parties within classical and quantum secret sharing and MPC protocols.