Posted

Prabhanjan Ananth, John Bostanci, Aditya Gulati, Yao-Ting Lin (Oct 07 2025).
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 QAC0{\sf 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(n1/c)O(n^{1/c}) bits of randomness, for any constant cc, if any family of strong pseudorandom unitaries exists.

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