Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913652654735360 |
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| author | Carolan, Joseph Poremba, Alexander |
| author_facet | Carolan, Joseph Poremba, Alexander |
| contents | Sponge hashing is a widely used class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a digest by once again iterating the block function on the final output bits. While much is known about the post-quantum security of the sponge construction when the block function is modeled as a random function or one-way permutation, the case of invertible permutations, which more accurately models the construction underlying SHA-3, has so far remained a fundamental open problem.
In this work, we make new progress towards overcoming this barrier and show several results. First, we prove the "double-sided zero-search" conjecture proposed by Unruh (eprint' 2021) and show that finding zero-pairs in a random $2n$-bit permutation requires at least $Ω(2^{n/2})$ many queries -- and this is tight due to Grover's algorithm. At the core of our proof lies a novel "symmetrization argument" which uses insights from the theory of Young subgroups. Second, we consider more general variants of the double-sided search problem and show similar query lower bounds for them. As an application, we prove the quantum one-wayness of the single-round sponge with invertible permutations in the quantum random oracle model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations Carolan, Joseph Poremba, Alexander Quantum Physics Cryptography and Security Sponge hashing is a widely used class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a digest by once again iterating the block function on the final output bits. While much is known about the post-quantum security of the sponge construction when the block function is modeled as a random function or one-way permutation, the case of invertible permutations, which more accurately models the construction underlying SHA-3, has so far remained a fundamental open problem. In this work, we make new progress towards overcoming this barrier and show several results. First, we prove the "double-sided zero-search" conjecture proposed by Unruh (eprint' 2021) and show that finding zero-pairs in a random $2n$-bit permutation requires at least $Ω(2^{n/2})$ many queries -- and this is tight due to Grover's algorithm. At the core of our proof lies a novel "symmetrization argument" which uses insights from the theory of Young subgroups. Second, we consider more general variants of the double-sided search problem and show similar query lower bounds for them. As an application, we prove the quantum one-wayness of the single-round sponge with invertible permutations in the quantum random oracle model. |
| title | Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations |
| topic | Quantum Physics Cryptography and Security |
| url | https://arxiv.org/abs/2403.04740 |