Pseudorandom (Function-Like) Quantum State Generators: New Definitions and Applications

Ananth, Prabhanjan; Gulati, Aditya; Qian, Luowen; Yuen, Henry

doi:10.1007/978-3-031-22318-1_9

Cited by 18 publications

(3 citation statements)

References 36 publications

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“…Concretely, we explore two applications: statistically binding and computationally hiding commitments, and pseudo one-time pads. While [AGQY22] previously demonstrated that these applications can be based on logarithmic PRS, we provide alternate proofs assuming the existence of QPRGs combined with Theorem 1.1. Moreover, our constructions resemble the textbook constructions of classical commitments and pseudo one-time pads and thus, are conceptually simpler than the ones presented by [AGQY22].…”

Section: Our Resultsmentioning

confidence: 99%

Cryptography from Pseudorandom Quantum States

Ananth

Qian

Yuen

2022

Lecture Notes in Computer Science

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A fundamental result in classical cryptography is that pseudorandom generators are equivalent to one-way functions and in fact implied by nearly every classical cryptographic primitive requiring computational assumptions. In this work, we consider a variant of pseudorandom generators called quantum pseudorandom generators (QPRGs), which are quantum algorithms that (pseudo)deterministically map short random seeds to long pseudorandom strings. We provide evidence that QPRGs can be as useful as PRGs by providing cryptographic applications of QPRGs such as commitments and encryption schemes.Our main result is showing that QPRGs can be constructed assuming the existence of logarithmic-length quantum pseudorandom states. This raises the possibility of basing QPRGs on assumptions weaker than one-way functions. We also consider quantum pseudorandom functions (QPRFs) and show that QPRFs can be based on the existence of logarithmic-length pseudorandom function-like states.Our primary technical contribution is a method for pseudodeterministically extracting uniformly random strings from Haar-random states.

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Section: Our Resultsmentioning

confidence: 99%

Cryptography from Pseudorandom Quantum States

Ananth

Qian

Yuen

2022

Lecture Notes in Computer Science

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“…2. If 𝒬 𝑛,𝑞,𝜆 consists of all possible 𝑞 computational basis states then this notion implies a pseudorandom function-like state generator (PRFSG) [AQY22,AGQY22].…”

Section: Our Resultsmentioning

confidence: 99%

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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“…The notion of pseudorandom states were first introduced by Ananth, Qian and Yuen in [AQY21]. A stronger definition where the adversary is allowed to make superposition queries to the challenge oracles was introduced in the follow-up work [AGQY23]. We reproduce their definition here:…”

Section: Pseudorandom Function-like State (Prfs) Generatorsmentioning

confidence: 99%

Encryption with Quantum Public Keys

Grilo¹,

Sattath²,

Vu³

2023

Preprint

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It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation can be constructed from one-way functions, whereas this is impossible in the classical setting in a black-box way.In this work, we study the question of building quantum public-key encryption schemes from one-way functions and even weaker assumptions. Firstly, we revisit the definition of IND-CPA security to this setting. Then, we propose three schemes for quantum public-key encryption from one-way functions, pseudorandom function-like states with proof of deletion and pseudorandom function-like states, respectively.

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Pseudorandom (Function-Like) Quantum State Generators: New Definitions and Applications

Cited by 18 publications

References 36 publications

Cryptography from Pseudorandom Quantum States

Cryptography from Pseudorandom Quantum States

Unclonable Encryption, Revisited

Encryption with Quantum Public Keys

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