Efficient simulation of random states and random unitaries
| Autor: | Gorjan Alagic, Christian Majenz, Alexander Russell |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pseudorandom number generator
FOS: Computer and information sciences Quantum Physics Computer Science - Cryptography and Security Theoretical computer science Ideal (set theory) Computer science 010102 general mathematics TheoryofComputation_GENERAL FOS: Physical sciences 01 natural sciences Unitary state Oracle Quantum state 0103 physical sciences Quantum algorithm 010307 mathematical physics 0101 mathematics Quantum Physics (quant-ph) Quantum Cryptography and Security (cs.CR) Quantum money PSPACE Computer Science::Cryptography and Security |
| Zdroj: | Advances in Cryptology – EUROCRYPT 2020 ISBN: 9783030457266 |
| DOI: | 10.48550/arxiv.1910.05729 |
| Popis: | We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered for restricted adversaries. Against adversaries with an a priori bound on the number of queries, it is well-known that $t$-designs suffice. Against polynomial-time adversaries, one can use pseudorandom states (PRS) and pseudorandom unitaries (PRU), as defined in a recent work of Ji, Liu, and Song; unfortunately, no provably secure construction is known for PRUs. In our setting, we are concerned with unbounded adversaries. Nonetheless, we are able to give stateful quantum algorithms which simulate the ideal object in both settings of interest. In the case of Haar-random states, our simulator is polynomial-time, has negligible error, and can also simulate verification and reflection through the simulated state. This yields an immediate application to quantum money: a money scheme which is information-theoretically unforgeable and untraceable. In the case of Haar-random unitaries, our simulator takes polynomial space, but simulates both forward and inverse access with zero error. These results can be seen as the first significant steps in developing a theory of lazy sampling for random quantum objects. Comment: 20+3 pages |
| Databáze: | OpenAIRE |
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