TY - GEN
T1 - The Power of a Single Haar Random State
T2 - 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2025
AU - Chen, Boyang
AU - Coladangelo, Andrea
AU - Sattath, Or
N1 - Publisher Copyright:
© International Association for Cryptologic Research 2025.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - In this work, we focus on the following question: what are the cryptographic implications of having access to an oracle that provides a single Haar random quantum state? We find that the study of such a model sheds light on several aspects of the notion of quantum pseudorandomness. Pseudorandom states are a family of states for which it is hard to distinguish between polynomially many copies of either a state sampled uniformly from the family or a Haar random state. A weaker notion, called single-copy pseudorandom states (1PRS), satisfies this property with respect to a single copy. We obtain the following results:First, we show, perhaps surprisingly, that 1PRS (as well as bit-commitments) exist relative to an oracle that provides a single Haar random state.Second, we build on this result to show the existence of an isometry oracle relative to which 1PRS exist, but PRS do not. First, we show, perhaps surprisingly, that 1PRS (as well as bit-commitments) exist relative to an oracle that provides a single Haar random state. Second, we build on this result to show the existence of an isometry oracle relative to which 1PRS exist, but PRS do not. Taken together, our contributions yield one of the first black-box separations between central notions of quantum pseudorandomness, and introduce a new framework to study black-box separations between various inherently quantum primitives.
AB - In this work, we focus on the following question: what are the cryptographic implications of having access to an oracle that provides a single Haar random quantum state? We find that the study of such a model sheds light on several aspects of the notion of quantum pseudorandomness. Pseudorandom states are a family of states for which it is hard to distinguish between polynomially many copies of either a state sampled uniformly from the family or a Haar random state. A weaker notion, called single-copy pseudorandom states (1PRS), satisfies this property with respect to a single copy. We obtain the following results:First, we show, perhaps surprisingly, that 1PRS (as well as bit-commitments) exist relative to an oracle that provides a single Haar random state.Second, we build on this result to show the existence of an isometry oracle relative to which 1PRS exist, but PRS do not. First, we show, perhaps surprisingly, that 1PRS (as well as bit-commitments) exist relative to an oracle that provides a single Haar random state. Second, we build on this result to show the existence of an isometry oracle relative to which 1PRS exist, but PRS do not. Taken together, our contributions yield one of the first black-box separations between central notions of quantum pseudorandomness, and introduce a new framework to study black-box separations between various inherently quantum primitives.
KW - Black-box separation
KW - Haar random states
KW - Quantum pseudorandomness
UR - https://www.scopus.com/pages/publications/105004793654
U2 - 10.1007/978-3-031-91098-2_5
DO - 10.1007/978-3-031-91098-2_5
M3 - Conference contribution
AN - SCOPUS:105004793654
SN - 9783031910975
T3 - Lecture Notes in Computer Science
SP - 108
EP - 137
BT - Advances in Cryptology – EUROCRYPT 2025 - 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
A2 - Fehr, Serge
A2 - Fouque, Pierre-Alain
PB - Springer Science and Business Media Deutschland GmbH
Y2 - 4 May 2025 through 8 May 2025
ER -