Compressed Permutation Oracles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909802108551168 |
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| author | Carolan, Joseph |
| author_facet | Carolan, Joseph |
| contents | The analysis of quantum algorithms which query random, invertible permutations has been a long-standing challenge in cryptography. Many techniques which apply to random oracles fail, or are not known to generalize to this setting. As a result, foundational cryptographic constructions involving permutations often lack quantum security proofs. With the aim of closing this gap, we develop and prove soundness of a compressed permutation oracle. Our construction shares many of the attractive features of Zhandry's original compressed function oracle: the purification is a small list of input-output pairs which meaningfully reflect an algorithm's knowledge of the oracle.
We then apply this framework to show that the Feistel construction with seven rounds is a strong quantum PRP, resolving an open question of (Zhandry, 2012). We further re-prove essentially all known quantum query lower bounds in the random permutation model, notably the collision and preimage resistance of both Sponge and Davies-Meyer, hardness of double-sided zero search and sparse predicate search, and give new lower bounds for cycle finding and the one-more problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_18586 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compressed Permutation Oracles Carolan, Joseph Quantum Physics Cryptography and Security The analysis of quantum algorithms which query random, invertible permutations has been a long-standing challenge in cryptography. Many techniques which apply to random oracles fail, or are not known to generalize to this setting. As a result, foundational cryptographic constructions involving permutations often lack quantum security proofs. With the aim of closing this gap, we develop and prove soundness of a compressed permutation oracle. Our construction shares many of the attractive features of Zhandry's original compressed function oracle: the purification is a small list of input-output pairs which meaningfully reflect an algorithm's knowledge of the oracle. We then apply this framework to show that the Feistel construction with seven rounds is a strong quantum PRP, resolving an open question of (Zhandry, 2012). We further re-prove essentially all known quantum query lower bounds in the random permutation model, notably the collision and preimage resistance of both Sponge and Davies-Meyer, hardness of double-sided zero search and sparse predicate search, and give new lower bounds for cycle finding and the one-more problem. |
| title | Compressed Permutation Oracles |
| topic | Quantum Physics Cryptography and Security |
| url | https://arxiv.org/abs/2509.18586 |