29 research outputs found
Quantum State Obfuscation from Classical Oracles
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 with a classical description and
an auxiliary quantum state , into a functionally-equivalent
obfuscated quantum program that hides as much as possible about and
. 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. 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
Quantum Tokens for Digital Signatures
The fisherman caught a quantum fish. "Fisherman, please let me go", begged
the fish, "and I will grant you three wishes". The fisherman agreed. The fish
gave the fisherman a quantum computer, three quantum signing tokens and his
classical public key. The fish explained: "to sign your three wishes, use the
tokenized signature scheme on this quantum computer, then show your valid
signature to the king, who owes me a favor".
The fisherman used one of the signing tokens to sign the document "give me a
castle!" and rushed to the palace. The king executed the classical verification
algorithm using the fish's public key, and since it was valid, the king
complied.
The fisherman's wife wanted to sign ten wishes using their two remaining
signing tokens. The fisherman did not want to cheat, and secretly sailed to
meet the fish. "Fish, my wife wants to sign ten more wishes". But the fish was
not worried: "I have learned quantum cryptography following the previous story
(The Fisherman and His Wife by the brothers Grimm). The quantum tokens are
consumed during the signing. Your polynomial wife cannot even sign four wishes
using the three signing tokens I gave you".
"How does it work?" wondered the fisherman. "Have you heard of quantum money?
These are quantum states which can be easily verified but are hard to copy.
This tokenized quantum signature scheme extends Aaronson and Christiano's
quantum money scheme, which is why the signing tokens cannot be copied".
"Does your scheme have additional fancy properties?" the fisherman asked.
"Yes, the scheme has other security guarantees: revocability, testability and
everlasting security. Furthermore, if you're at sea and your quantum phone has
only classical reception, you can use this scheme to transfer the value of the
quantum money to shore", said the fish, and swam away.Comment: Added illustration of the abstract to the ancillary file
Indistinguishability Obfuscation of Null Quantum Circuits and Applications
We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming:
- The quantum hardness of learning with errors (LWE).
- Post-quantum indistinguishability obfuscation for classical circuits.
- A notion of "dual-mode" classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM).
Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP
Hamiltonian simulation with optimal sample complexity
© 2017 Author(s). We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631-633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.S.K. and C.Y.L. are funded by the Department of Defense. G.H.L. is funded by the NSF CCR and the ARO quantum computing projects. M.O. acknowledges Leverhulme Trust Early Career Fellowship (ECF-2015-256) and European Union project QALGO (Grant Agreement No. 600700) for financial support. T.J.Y. thanks the DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. The authors are grateful to the University of Maryland Libraries’ Open Access Publishing Fund and the Massachusetts Institute of Technology Open Access Publishing Fund for partial funding for open access
Impossibility of Quantum Virtual Black-Box Obfuscation of Classical Circuits
Virtual black-box obfuscation is a strong cryptographic primitive: it
encrypts a circuit while maintaining its full input/output functionality. A
remarkable result by Barak et al. (Crypto 2001) shows that a general obfuscator
that obfuscates classical circuits into classical circuits cannot exist. A
promising direction that circumvents this impossibility result is to obfuscate
classical circuits into quantum states, which would potentially be better
capable of hiding information about the obfuscated circuit. We show that, under
the assumption that learning-with-errors (LWE) is hard for quantum computers,
this quantum variant of virtual black-box obfuscation of classical circuits is
generally impossible. On the way, we show that under the presence of dependent
classical auxiliary input, even the small class of classical point functions
cannot be quantum virtual black-box obfuscated.Comment: v2: Add the notion of decomposable public keys, which allows our
impossibility to hold without assuming circular security for QFHE. We also
fix an auxiliary lemma (2.9 in v2) where a square root was missing (this does
not influence the main result
Quantum State Obfuscation from Classical Oracles
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 with a classical description and an auxiliary quantum state , into a functionally-equivalent obfuscated quantum program that hides as much as possible about and . 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\u27\u27 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 (\LM) quantum program: an alternating sequence of CNOT operations and partial ZX measurements
Quantum delegation from fully homomorphic encryption based on Ring learning with errors
Quantum computers will not likely be widespread and accessible to everyone in a foreseen future. Being capable of delegating quantum computation to untrusted parties while not losing condentiality would individuals to grant access to this technology. On the other hand, many current cryptography applications rely on the hardness of solving the discrete logarithm or integer factorization among other related problems that can be eciently solved by quantum computers. Lattice-based cryptography is one of the most promising approaches in the post-quantum cryptography eld due to the hardness of breaking certain lattices problems with the aid of quantum computers like the Learning With Errors problem or its ring variant, the Ring Learning With Errors problem. We propose and prove security of a new levelled fully homomorphic lattice-based encryption scheme for encrypting the classical keys of the quantum homomorphic encryption schemes in the literature based on the RLWE problem. Moreover, in this work we do a survey on quantum homomorphic encryption which provides a toolkit for outsourcing quantum computations securely