TY - GEN
T1 - Real-Valued Somewhat-Pseudorandom Unitaries
AU - Brakerski, Zvika
AU - Magrafta, Nir
N1 - Publisher Copyright: © International Association for Cryptologic Research 2025.
PY - 2025
Y1 - 2025
N2 - We explore a very simple distribution of unitaries: random (binary) phase—Hadamard—random (binary) phase—random computational-basis permutation. We show that this distribution is statistically indistinguishable from random Haar unitaries for any polynomial set of orthogonal input states (in any basis) with polynomial multiplicity. This shows that even though real-valued unitaries cannot be completely pseudorandom (Haug, Bharti, Koh, arXiv:2306.11677), we can still obtain some pseudorandom properties without giving up on the simplicity of a real-valued unitary. Our analysis shows that an even simpler construction: applying a random (binary) phase followed by a random computational-basis permutation, would suffice, assuming that the input is orthogonal and flat (that is, has high min-entropy when measured in the computational basis). Using quantum-secure one-way functions (which imply quantum-secure pseudorandom functions and permutations), we obtain an efficient cryptographic instantiation of the above.
AB - We explore a very simple distribution of unitaries: random (binary) phase—Hadamard—random (binary) phase—random computational-basis permutation. We show that this distribution is statistically indistinguishable from random Haar unitaries for any polynomial set of orthogonal input states (in any basis) with polynomial multiplicity. This shows that even though real-valued unitaries cannot be completely pseudorandom (Haug, Bharti, Koh, arXiv:2306.11677), we can still obtain some pseudorandom properties without giving up on the simplicity of a real-valued unitary. Our analysis shows that an even simpler construction: applying a random (binary) phase followed by a random computational-basis permutation, would suffice, assuming that the input is orthogonal and flat (that is, has high min-entropy when measured in the computational basis). Using quantum-secure one-way functions (which imply quantum-secure pseudorandom functions and permutations), we obtain an efficient cryptographic instantiation of the above.
UR - http://www.scopus.com/inward/record.url?scp=85211434022&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-031-78017-2_2
DO - https://doi.org/10.1007/978-3-031-78017-2_2
M3 - منشور من مؤتمر
SN - 9783031780165
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 36
EP - 59
BT - Theory of Cryptography - 22nd International Conference, TCC 2024, Proceedings
A2 - Boyle, Elette
A2 - Mahmoody, Mohammad
PB - Springer Science and Business Media B.V.
T2 - 22nd Theory of Cryptography Conference, TCC 2024
Y2 - 2 December 2024 through 6 December 2024
ER -