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Title:
Gluing Random Unitaries with Inverses and Applications to Strong Pseudorandom Unitaries
Authors: Prabhanjan Ananth, John Bostanci, Aditya Gulati, Yao-Ting Lin
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 \mathsf{QAC0} [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 O(n^{1/c}) bits of randomness, for any constant c, if any family of strong pseudorandom unitaries exists.
ePrint: https://eprint.iacr.org/2025/1889
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