On the Cryptographic Futility of Non-Collapsing Measurements

• URL: http://arxiv.org/abs/2510.05055v1
• Date: Mon, 06 Oct 2025 17:36:22 GMT
• Title: On the Cryptographic Futility of Non-Collapsing Measurements
• Authors: Alper Cakan, Dakshita Khurana, Tomoyuki Morimae, Yuki Shirakawa, Kabir Tomer, Takashi Yamakawa,
• Abstract summary: We investigate quantum analogues of collision resistance and obtain separations between quantum one-way'' and collision-resistant'' primitives.
• Score: 13.234610219099102
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate quantum analogues of collision resistance and obtain separations between quantum ``one-way'' and ``collision-resistant'' primitives. 1. Our first result studies one-wayness versus collision-resistance defined over quantum circuits that output classical strings. We show that there is a classical oracle $\mathcal{O}$ relative to which (sub-exponentially secure) indistinguishability obfuscation and one-way permutations exist even against adversaries that make quantum queries to a non-collapsing measurement oracle, $\mathcal{Q}^{\mathcal{O}}$. Very roughly, $\mathcal{Q}^{\mathcal{O}}$ outputs the result of multiple non-collapsing measurements on the output of any quantum $\mathcal{O}$-aided circuit. This rules out fully black-box {\em quantum} constructions of $Y$ from $X$ for any $X \in \{$indistinguishability obfuscation and one-way permutations, public-key encryption, deniable encryption, oblivious transfer, non-interactive ZK, trapdoor permutations, quantum money$\}, Y \in \{$collision-resistant hash functions, hard problems in SZK, homomorphic encryption, distributional collision-resistant puzzles$\}$. 2. Our second result studies one-wayness versus collision-resistance defined over quantum states. Here, we show that relative to the same classical oracle $\mathcal{O}$, (sub-exponentially secure) indistinguishability obfuscation and one-way permutations exist even against adversaries that make quantum queries to a {\em cloning unitary} $\mathsf{QCol}^\mathcal{O}$. Very roughly, this latter oracle implements a well-defined, linear operation to clone a subset of the qubits output by any quantum $\mathcal{O}$-aided circuit. This rules out fully black-box constructions of quantum lightning from public-key quantum money.

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