In classical computing, garbled circuits (and their generalization known as randomized encodings) are a versatile cryptographic tool with many applications such as secure multiparty computation, delegated computation, depth-reduction of cryptographic primitives, complexity lower-bounds, and more. Quantum analogues of garbled circuits were not known prior to this work.
Garbled circuits is a cryptographic technique, which has been used among other things for the construction of two and threeparty secure computation, private function evaluation and secure outsourcing. Garbling schemes is a primitive which formalizes the syntax and security properties of garbled circuits. We define a generalization of garbling schemes called reactive garbling schemes. We consider functions and garbled functions taking multiple inputs and giving multiple outputs. Two garbled functions can be linked together: an encoded output of one garbled function can be transformed into an encoded input of the other garbled function without communication between the parties. Reactive garbling schemes also allow partial evaluation of garbled functions even when only some of the encoded inputs are provided. It is possible to further evaluate the linked garbled functions when more garbled inputs become available. It is also possible to later garble more functions and link them to the ongoing garbled evaluation. We provide rigorous definitions for reactive garbling schemes. We define a new notion of security for reactive garbling schemes called confidentiality. We provide both simulation based and indistinguishability based notions of security. We also show that the simulation based notion of security implies the indistinguishability based notion of security. We present an instantiation of reactive garbling schemes. We present an application of reactive garbling schemes to reactive two-party computation secure against a malicious, static adversary. We demonstrate how garbling schemes can be used to give abstract black-box descriptions and proof of several advanced applications of garbled circuits in the literature, including Minilego and Lindell’s forge-and-lose technique.
Randomized encoding is a powerful cryptographic primitive with various applications such as secure multiparty computation, verifiable computation, parallel cryptography, and complexity lower bounds. Intuitively, randomized encoding
f^ of a function
f is another function such that
f(x) can be recovered from
f^(x), and nothing except for
f(x) is leaked from
f^(x). Its quantum version, quantum randomized encoding, has been introduced recently [Brakerski and Yuen, arXiv:2006.01085]. Intuitively, quantum randomized encoding
F^ of a quantum operation
F is another quantum operation such that, for any quantum state
ρ,
F(ρ) can be recovered from
F^(ρ), and nothing except for
F(ρ) is leaked from
F^(ρ). In this paper, we show three results. First, we show that if quantum randomized encoding of BB84 state generations is possible with an encoding operation
E, then a two-round verification of quantum computing is possible with a classical verifier who can additionally do the operation
E. One of the most important goals in the field of the verification of quantum computing is to construct a verification protocol with a verifier as classical as possible. This result therefore demonstrates a potential application of quantum randomized encoding to the verification of quantum computing: if we can find a good quantum randomized encoding (in terms of the encoding complexity), then we can construct a good verification protocol of quantum computing. Our second result is, however, to show that too good quantum randomized encoding is impossible: if quantum randomized encoding for the generation of even simple states (such as BB84 states) is possible with a classical encoding operation, then the no-cloning is violated. Finally, we consider a natural modification of blind quantum computing protocols in such a way that the server gets the output like quantum randomized encoding. We show that the modified protocol is not secure.
The universal blind quantum computation protocol (UBQC) enables an almost classical client to delegate a quantum computation to an untrusted quantum server (in the form of a garbled quantum circuit) while the security for the client is unconditional. In this contribution, we explore the possibility of extending the verifiable UBQC, to achieve further functionalities following the analogous research for classical circuits (Yao 1986). First, exploring the asymmetric nature of UBQC (the client preparing only single qubits, while the server runs the entire quantum computation), we present a “Yao”-type protocol for secure two-party quantum computation. Similar to the classical setting, our quantum Yao protocol is secure against a specious (quantum honest-but-curious) garbler, but in our case, against a (fully) malicious evaluator. Unlike the previous work on quantum two-party computation of Dupuis et al., 2010, we do not require any online-quantum communication between the garbler and the evaluator and, thus, no extra cryptographic primitive. This feature will allow us to construct a simple universal one-time compiler for any quantum computation using one-time memory, in a similar way to the classical work of Goldwasser et al., 2008, while more efficiently than the previous work of Broadbent et al., 2013.
Abstract. Garbled circuits is a cryptographic technique, which has been used among other things for the con-struction of two and three-party secure computation, private function evaluation and secure outsourcing. Garbling schemes is a primitive which formalizes the syntax and security properties of garbled circuits. We dene a gener-alization of garbling schemes called reactive garbling schemes. We consider functions and garbled functions taking multiple inputs and giving multiple outputs. Two garbled functions can be linked together: an encoded output of one garbled function can be transformed into an encoded input of the other garbled function without commu-nication between the parties. Reactive garbling schemes also allow partial evaluation of garbled functions even when only some of the encoded inputs are provided. It is possible to further evaluate the linked garbled functions when more garbled inputs become available. It is also possible to later garble more functions and link them to the ongoing garbled evaluation. We provide rigorous denitions for reactive garbling schemes. We dene a new notion of security for reactive garbling schemes called condentiality. We provide both simulation based and in-distinguishability based notions of security. We also show that the simulation based notion of security implies the indistinguishability based notion of security. We present an instantiation of reactive garbling schemes. We present an application of reactive garbling schemes to reactive two-party computation secure against a malicious adversary. We demonstrate how garbling schemes can be used to give abstract black-box descriptions and proof of several advanced applications of garbled circuits in the literature, including Minilego and Lindell’s forge-and-loose technique. 1
Protocols for secure computation enable mutually distrustful parties to jointly compute on their private inputs without revealing anything but the result. Over recent years, secure computation has become practical and considerable effort has been made to make it more and more efficient. A highly important tool in the design of two-party protocols is Yao's garbled circuit construction (Yao 1986), and multiple optimizations on this primitive have led to performance improvements of orders of magnitude over the last years. However, many of these improvements come at the price of making very strong assumptions on the underlying cryptographic primitives being used (e.g., that AES is secure for related keys, that it is circular secure, and even that it behaves like a random permutation when keyed with a public fixed key). The justification behind making these strong assumptions has been that otherwise it is not possible to achieve fast garbling and thus fast secure computation. In this paper, we take a step back and examine whether it is really the case that such strong assumptions are needed. We provide new methods for garbling that are secure solely under the assumption that the primitive used (e.g., AES) is a pseudorandom function. Our results show that in many cases, the penalty incurred is not significant, and so a more conservative approach to the assumptions being used can be adopted.
Protocols for secure computation enable mutually distrustful parties to jointly compute on their private inputs without revealing anything but the result. Over recent years, secure com-putation has become practical and considerable effort has been made to make it more and more efficient. A highly important tool in the design of two-party protocols is Yao’s garbled circuit construction (Yao 1986), and multiple optimizations on this primitive have led to performance improvements of orders of magnitude over the last years. However, many of these improvements come at the price of making very strong assumptions on the underlying cryptographic primitives being used (e.g., that AES is secure for related keys, that it is circular secure, and even that it behaves like a random permutation when keyed with a public fixed key). The justification behind making these strong assumptions has been that otherwise it is not possible to achieve fast garbling and thus fast secure computation. In this paper, we take a step back and examine whether it is really the case that such strong assumptions are needed. We provide new methods for garbling that are secure solely under the assumption that the primitive used (e.g., AES) is a pseudorandom function. Our results show that in many cases, the penalty incurred is not significant, and so a more conservative approach to the assumptions being used can be adopted.