Gluing Random Unitaries with Inverses and Applications to Strong Pseudorandom Unitaries
Abstract
Gluing theorem for random unitaries [Schuster, Haferkamp, Huang, QIP 2025] have found numerous applications, including designing low depth random unitaries [Schuster, Haferkamp, Huang, QIP 2025], random unitaries in [Foxman, Parham, Vasconcelos, Yuen'25] and generically shortening the key length of pseudorandom unitaries [Ananth, Bostanci, Gulati, Lin EUROCRYPT'25]. We present an alternate method of combining Haar random unitaries from the gluing lemma from [Schuster, Haferkamp, Huang, QIP 2025] that is secure against adversaries with inverse query access to the joined unitary. As a consequence, we show for the first time that strong pseudorandom unitaries can generically have their length extended, and can be constructed using only bits of randomness, for any constant , if any family of strong pseudorandom unitaries exists.
Cite
@article{arxiv.2510.04085,
title = {Gluing Random Unitaries with Inverses and Applications to Strong Pseudorandom Unitaries},
author = {Prabhanjan Ananth and John Bostanci and Aditya Gulati and Yao-Ting Lin},
journal= {arXiv preprint arXiv:2510.04085},
year = {2025}
}
Comments
55 pages. A preliminary version, merging this paper and arXiv:2509.24432, appears in the proceedings of the 45th Annual International Cryptology Conference (CRYPTO 2025) under the title "Pseudorandom Unitaries in the Haar Random Oracle Model". This is Part II of the full version