A Note on the Common Haar State Model

Common random string model is a popular model in classical cryptography with many constructions proposed in this model. We study a quantum analogue of this model called the common Haar state model, which was also studied in an independent work by Chen, Coladangelo and Sattath (arXiv 2024). In this m...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Prabhanjan Ananth, Gulati, Aditya, Yao-Ting, Lin
Format: Article
Language:English
Subjects:
Cryptography
Lower bounds
Pseudorandom
Online Access:Get full text
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Summary:Common random string model is a popular model in classical cryptography with many constructions proposed in this model. We study a quantum analogue of this model called the common Haar state model, which was also studied in an independent work by Chen, Coladangelo and Sattath (arXiv 2024). In this model, every party in the cryptographic system receives many copies of one or more i.i.d Haar states. Our main result is the construction of a statistically secure PRSG with: (a) the output length of the PRSG is strictly larger than the key size, (b) the security holds even if the adversary receives \(O\left(\frac{\lambda}{(\log(\lambda))^{1.01}} \right)\) copies of the pseudorandom state. We show the optimality of our construction by showing a matching lower bound. Our construction is simple and its analysis uses elementary techniques.
ISSN:2331-8422