Scalable Pseudorandom Quantum States

Brakerski, Zvika; Shmueli, Omri

doi:10.1007/978-3-030-56880-1_15

Cited by 13 publications

(15 citation statements)

References 8 publications

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“…Pseudorandom quantum states [31][32][33] are sets of quantum states that can be efficiently generated but computationally indistinguishable from Haar random states. (The formal definition is given in Definition 1.)…”

Section: B Our Resultsmentioning

confidence: 99%

“…Let us review pseudorandom quantum states [31][32][33]. Intuitively, pseudorandom quantum states {|φ k } k are sets of quantum states such that each state |φ k is efficiently generated on input k, but |φ k ⊗t is computationally indistinguishable from t copies of a Haar random state.…”

Section: B Pseudorandom Quantum Statesmentioning

confidence: 99%

“…Note that in this paper, we assume m ≥ cn for a constant c > 1. Although it is possible to construct PRS without this restriction [33], this is satisfied in the construction of Ref. [34,39].…”

Section: B Pseudorandom Quantum Statesmentioning

confidence: 99%

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Quantum commitments and signatures without one-way functions

Morimae¹,

Yamakawa²

2021

Preprint

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Section: B Our Resultsmentioning

confidence: 99%

Section: B Pseudorandom Quantum Statesmentioning

confidence: 99%

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Quantum commitments and signatures without one-way functions

Morimae¹,

Yamakawa²

2021

Preprint

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“…With this approach, one can construct computationally secure n-qubit PRS which is also desired for unforgeability security property. Nevertheless, as discussed in [11], these methods are not scalable and also an n-qubit PRS generator cannot necessarily be used to produce a random state for k-qubit where k < n. For these reasons, in [11] the authors introduce a scalable construction for PRS which, unlike prior works, relies on randomising the amplitudes of the states instead of the phase. The authors use Gaussian sampling methods to efficiently achieve PRS.…”

Section: Efficient Unforgeability With Prsmentioning

confidence: 99%

“…However, unlike the classical case, the relation between the quantum pseudorandomness and the quantum PUFs is not well-explored. The existing PRS schemes are constructed under computational assumptions such as quantum-secure PRF or quantum secure one-way functions [11,9]. An interesting question which arises is whether quantum pseudorandomness can be achieved under a different set of assumptions?…”

Section: Introductionmentioning

confidence: 99%

On the Connection Between Quantum Pseudorandomness and Quantum Hardware Assumptions

Doosti¹,

Kashefi²,

Chakraborty³

2021

Preprint

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This paper, for the first time, addresses the questions related to the connections between the quantum pseudorandomness and quantum hardware assumptions, specifically quantum physical unclonable functions (qPUFs). Our results show that the efficient pseudorandom quantum states (PRS) are sufficient to construct the challenge set for the universally unforgeable qPUF, improving the previous existing constructions that are based on the Haar-random states. We also show that both the qPUFs and the quantum pseudorandom unitaries (PRUs) can be constructed from each other, providing new ways to obtain PRS from the hardware assumptions. Moreover, we provide a sufficient condition (in terms of the diamond norm) that a set of unitaries should have to be a PRU in order to construct a universally unforgeable qPUF, giving yet another novel insight into the properties of the PRUs. Later, as an application of our results, we show that the efficiency of an existing qPUF-based client-server identification protocol can be improved without losing the security requirements of the protocol.

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Unclonable Encryption, Revisited

Ananth

Kaleoglu

2021

Lecture Notes in Computer Science

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We introduce a new notion called 𝒬-secure pseudorandom isometries (PRI). A pseudorandom isometry is an efficient quantum circuit that maps an 𝑛-qubit state to an (𝑛 + 𝑚)-qubit state in an isometric manner. In terms of security, we require that the output of a 𝑞-fold PRI on 𝜌, for 𝜌 ∈ 𝒬, for any polynomial 𝑞, should be computationally indistinguishable from the output of a 𝑞-fold Haar isometry on 𝜌.By fine-tuning 𝒬, we recover many existing notions of pseudorandomness. We present a construction of PRIs and assuming post-quantum one-way functions, we prove the security of 𝒬-secure pseudorandom isometries (PRI) for different interesting settings of 𝒬.We also demonstrate many cryptographic applications of PRIs, including, length extension theorems for quantum pseudorandomness notions, message authentication schemes for quantum states, multi-copy secure public and private encryption schemes, and succinct quantum commitments.

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Scalable Pseudorandom Quantum States

Cited by 13 publications

References 8 publications

Quantum commitments and signatures without one-way functions

Quantum commitments and signatures without one-way functions

On the Connection Between Quantum Pseudorandomness and Quantum Hardware Assumptions

Unclonable Encryption, Revisited

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