An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.
An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.
An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.
An indistinguishability obfuscator is a probabilistic polynomial-time algorithm that takes a circuit as input and outputs a new circuit that has the same functionality as the input circuit, such that for any two circuits of the same size that compute the same function, the outputs of the indistinguishability obfuscator are computationally indistinguishable. Here, we study schemes for indistinguishability obfuscation for quantum circuits (qiO), which consists in a procedure that takes as input a quantum circuit and outputs a quantum state, together with a quantum circuit, which together can be used to evaluate the original quantum circuit on any quantum input; the security guarantee being that for two quantum circuits of the same size that have the same input-output behaviour, the outputs of the obfuscator are computationally indistinguishable. Our main result provides a construction for qiO, where the size of the output of the obfuscator is exponential in the number of non-Clifford (T gates), which means that the construction is efficient as long as the number of T gates is logarithmic in the circuit size.
A major unresolved question in quantum cryptography is whether it is possible to obfuscate arbitrary quantum computation. Indeed, there is much yet to understand about the feasibility of quantum obfuscation even in the classical oracle model, where one is given for free the ability to obfuscate any classical circuit. In this work, we develop a new array of techniques that we use to construct a quantum state obfuscator, a powerful notion formalized recently by Coladangelo and Gunn (arXiv:2311.07794) in their pursuit of better software copy-protection schemes. Quantum state obfuscation refers to the task of compiling a quantum program, consisting of a quantum circuit C with a classical description and an auxiliary quantum state ψ, into a functionally-equivalent obfuscated quantum program that hides as much as possible about C and ψ. We prove the security of our obfuscator when applied to any pseudo-deterministic quantum program, i.e. one that computes a (nearly) deterministic classical input / classical output functionality. Our security proof is with respect to an efficient classical oracle, which may be heuristically instantiated using quantum-secure indistinguishability obfuscation for classical circuits. Our result improves upon the recent work of Bartusek, Kitagawa, Nishimaki and Yamakawa (STOC 2023) who also showed how to obfuscate pseudo-deterministic quantum circuits in the classical oracle model, but only ones with a completely classical description. Furthermore, our result answers a question of Coladangelo and Gunn, who provide a construction of quantum state indistinguishability obfuscation with respect to a quantum oracle, but leave the existence of a concrete real-world candidate as an open problem. Indeed, our quantum state obfuscator together with Coladangelo-Gunn gives the first candidate realization of a “best-possible” copy-protection scheme for all polynomial-time functionalities. Our techniques deviate significantly from previous works on quantum obfuscation. We develop several novel technical tools which we expect to be broadly useful in quantum cryptography. These tools include a publicly-verifiable, linearly-homomorphic quantum authentication scheme with classically-decodable ZX measurements (which we build from coset states), and a method for compiling any quantum circuit into a ”linear + measurement” () quantum program: an alternating sequence of CNOT operations and partial ZX measurements.
Encryption of data is fundamental to secure communication in the modern world. Beyond encryption of data lies obfuscation, i.e., encryption of functionality. It is well-known that the most powerful means of obfuscating classical programs, so-called ``black-box obfuscation',' is provably impossible [Barak et al '12]. However, several recent results have yielded candidate schemes that satisfy a definition weaker than black-box, and yet still have numerous applications. In this work, we initialize the rigorous study of obfuscating programs via quantum-mechanical means. We define notions of quantum obfuscation which encompass several natural variants. The input to the obfuscator can describe classical or quantum functionality, and the output can be a circuit description or a quantum state. The obfuscator can also satisfy one of a number of obfuscation conditions: black-box, information-theoretic black-box, indistinguishability, and best possible; the last two conditions come in three variants: perfect, statistical, and computational. We discuss many applications, including CPA-secure quantum encryption, quantum fully-homomorphic encryption, and public-key quantum money. We then prove several impossibility results, extending a number of foundational papers on classical obfuscation to the quantum setting. We prove that quantum black-box obfuscation is impossible in a setting where adversaries can possess more than one output of the obfuscator. In particular, generic transformation of quantum circuits into black-box-obfuscated quantum circuits is impossible. We also show that statistical indistinguishability obfuscation is impossible, up to an unlikely complexity-theoretic collapse. Our proofs involve a new tool: chosen-ciphertext-secure encryption of quantum data, which was recently shown to be possible assuming quantum-secure one-way functions exist [Alagic et al '16].
Research on quantum cryptography has burgeoned in the recent decades and combined quantum mechanics and cryptography theory. Among the existing quantum cryptographic primitives, quantum obfuscation is an emergent force to be reckoned with. Quantum obfuscation means obfuscating a circuit by quantum mechanics to improve security. It is used to hide functionality and prevent the reverse engineering of quantum circuits. However, research studies on the construction of quantum obfuscation are relatively immature due to its difficulty in implementation and application. Also, the obfuscation for quantum non-linear functions has not been suggested yet, although quantum non-linear functions cover a wide range of quantum functions that can be obfuscated. In this paper, we initiate a universal definition of quantum obfuscation which utilizes quantum teleportation to construct an obfuscator and interpreter for quantum non-linear functions. Furthermore, we demonstrate the validity of applying the obfuscation to the quantum asymmetric encryption scheme and rigorously prove that the encryption realized by quantum obfuscation satisfies IND (indistinguishability)-security. This work provides a positive possibility of quantum obfuscation for quantum non-linear functions and will complement the theory of both quantum obfuscation and quantum asymmetric encryption.
Quantum computing solutions are increasingly deployed in commercial environments through delegated computing, especially one of the most critical issues is to guarantee the confidentiality and proprietary of quantum implementations. Since the proposal of general-purpose indistinguishability obfuscation (iO) and functional encryption schemes, iO has emerged as a seemingly versatile cryptography primitive. Existing research on quantum indistinguishable obfuscation (QiO) primarily focuses on task-oriented, lacking solutions to general quantum computing. In this paper, we propose a scheme for constructing QiO via the equivalence of quantum circuits. It introduces the concept of quantum subpath sum equivalence, demonstrating that indistinguishability between two quantum circuits can be achieved by incremental changes in quantum subpaths. The restriction of security loss is solved by reducing the distinguisher to polynomial probability test. The scheme obfuscates the quantum implementation of classical functions in a path-sum specification, ensuring the indistinguishability between different quantum implementations. The results demonstrate the feasibility of indistinguishability obfuscation for general circuits and provide novel insights on intellectual property protection and secure delegated quantum computing.