3,854 research outputs found
Semantic Security and Indistinguishability in the Quantum World
At CRYPTO 2013, Boneh and Zhandry initiated the study of quantum-secure
encryption. They proposed first indistinguishability definitions for the
quantum world where the actual indistinguishability only holds for classical
messages, and they provide arguments why it might be hard to achieve a stronger
notion. In this work, we show that stronger notions are achievable, where the
indistinguishability holds for quantum superpositions of messages. We
investigate exhaustively the possibilities and subtle differences in defining
such a quantum indistinguishability notion for symmetric-key encryption
schemes. We justify our stronger definition by showing its equivalence to novel
quantum semantic-security notions that we introduce. Furthermore, we show that
our new security definitions cannot be achieved by a large class of ciphers --
those which are quasi-preserving the message length. On the other hand, we
provide a secure construction based on quantum-resistant pseudorandom
permutations; this construction can be used as a generic transformation for
turning a large class of encryption schemes into quantum indistinguishable and
hence quantum semantically secure ones. Moreover, our construction is the first
completely classical encryption scheme shown to be secure against an even
stronger notion of indistinguishability, which was previously known to be
achievable only by using quantum messages and arbitrary quantum encryption
circuits.Comment: 37 pages, 2 figure
Quantum Fully Homomorphic Encryption With Verification
Fully-homomorphic encryption (FHE) enables computation on encrypted data
while maintaining secrecy. Recent research has shown that such schemes exist
even for quantum computation. Given the numerous applications of classical FHE
(zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is
reasonable to hope that quantum FHE (or QFHE) will lead to many new results in
the quantum setting. However, a crucial ingredient in almost all applications
of FHE is circuit verification. Classically, verification is performed by
checking a transcript of the homomorphic computation. Quantumly, this strategy
is impossible due to no-cloning. This leads to an important open question: can
quantum computations be delegated and verified in a non-interactive manner? In
this work, we answer this question in the affirmative, by constructing a scheme
for QFHE with verification (vQFHE). Our scheme provides authenticated
encryption, and enables arbitrary polynomial-time quantum computations without
the need of interaction between client and server. Verification is almost
entirely classical; for computations that start and end with classical states,
it is completely classical. As a first application, we show how to construct
quantum one-time programs from classical one-time programs and vQFHE.Comment: 30 page
Neural network agent playing spin Hamiltonian games on a quantum computer
Quantum computing is expected to provide new promising approaches for solving
the most challenging problems in material science, communication, search,
machine learning and other domains. However, due to the decoherence and gate
imperfection errors modern quantum computer systems are characterized by a very
complex, dynamical, uncertain and fluctuating computational environment. We
develop an autonomous agent effectively interacting with such an environment to
solve magnetism problems. By using the reinforcement learning the agent is
trained to find the best-possible approximation of a spin Hamiltonian ground
state from self-play on quantum devices. We show that the agent can learn the
entanglement to imitate the ground state of the quantum spin dimer. The
experiments were conducted on quantum computers provided by IBM. To compensate
the decoherence we use local spin correction procedure derived from a general
sum rule for spin-spin correlation functions of a quantum system with even
number of antiferromagnetically-coupled spins in the ground state. Our study
paves a way to create a new family of the neural network eigensolvers for
quantum computers.Comment: Local spin correction procedure was used to compensate real device
errors; comparison with variational approach was adde
Perfect zero knowledge for quantum multiprover interactive proofs
In this work we consider the interplay between multiprover interactive
proofs, quantum entanglement, and zero knowledge proofs - notions that are
central pillars of complexity theory, quantum information and cryptography. In
particular, we study the relationship between the complexity class MIP, the
set of languages decidable by multiprover interactive proofs with quantumly
entangled provers, and the class PZKMIP, which is the set of languages
decidable by MIP protocols that furthermore possess the perfect zero
knowledge property.
Our main result is that the two classes are equal, i.e., MIP
PZKMIP. This result provides a quantum analogue of the celebrated result of
Ben-Or, Goldwasser, Kilian, and Wigderson (STOC 1988) who show that MIP
PZKMIP (in other words, all classical multiprover interactive protocols can be
made zero knowledge). We prove our result by showing that every MIP
protocol can be efficiently transformed into an equivalent zero knowledge
MIP protocol in a manner that preserves the completeness-soundness gap.
Combining our transformation with previous results by Slofstra (Forum of
Mathematics, Pi 2019) and Fitzsimons, Ji, Vidick and Yuen (STOC 2019), we
obtain the corollary that all co-recursively enumerable languages (which
include undecidable problems as well as all decidable problems) have zero
knowledge MIP protocols with vanishing promise gap
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