Fiat-Shamir for Proofs Lacks a Proof Even in the Presence of Shared Entanglement

by   Frédéric Dupuis, et al.

We explore the cryptographic power of arbitrary shared physical resources. The most general such resource is access to a fresh entangled quantum state at the outset of each protocol execution. We call this the Common Reference Quantum State (CRQS) model, in analogy to the well-known Common Reference String (CRS). The CRQS model is a natural generalization of the CRS model but appears to be more powerful: in the two-party setting, a CRQS can sometimes exhibit properties associated with a Random Oracle queried once by measuring a maximally entangled state in one of many mutually unbiased bases. We formalize this notion as a Weak One-Time Random Oracle (WOTRO), where we only ask of the m-bit output to have some randomness when conditioned on the n-bit input. We show that WOTRO with n - m ∈ω( n) is black-box impossible in the CRQS model, meaning that no protocol can have its security black-box reduced to a cryptographic game. We define a (inefficient) quantum adversary against any WOTRO protocol that can be efficiently simulated in polynomial time, ruling out any reduction to a secure game that only makes black-box queries to the adversary. On the other hand, we introduce a non-game quantum assumption for hash functions that implies WOTRO in the CRQ$ model (where the CRQS consists only of EPR pairs). We first build a statistically secure WOTRO protocol where m = n, then hash the output. The impossibility of WOTRO has the following consequences. First, we show the black-box impossibility of a quantum Fiat-Shamir transform, extending the impossibility result of Bitansky et al. (TCC '13) to the CRQS model. Second, we show a black-box impossibility result for a strenghtened version of quantum lightning (Zhandry, Eurocrypt '19) where quantum bolts have an additional parameter that cannot be changed without generating new bolts.



page 1

page 2

page 3

page 4


Post-Quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-Round

From the minimal assumption of post-quantum semi-honest oblivious transf...

Fast Black-Box Quantum State Preparation

Quantum state preparation is an important ingredient for other higher-le...

Impossibility of Quantum Virtual Black-Box Obfuscation of Classical Circuits

Virtual black-box obfuscation is a strong cryptographic primitive: it en...

A Private Quantum Bit String Commitment

We propose an entanglement-based quantum bit string commitment protocol ...

Distributional Collision Resistance Beyond One-Way Functions

Distributional collision resistance is a relaxation of collision resista...

Certifiable Randomness from a Single Quantum Device

We give a protocol for producing certifiable randomness from a single un...

Efficient simulation of random states and random unitaries

We consider the problem of efficiently simulating random quantum states ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.