Compiling Any $\mathsf{MIP}^{*}$ into a (Succinct) Classical Interactive Argument
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909856011649024 |
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| author | Huang, Andrew Kalai, Yael Tauman |
| author_facet | Huang, Andrew Kalai, Yael Tauman |
| contents | We present a generic compiler that converts any $\mathsf{MIP}^{*}$ protocol into a succinct interactive argument where the communication and the verifier are classical, and where post-quantum soundness relies on the post-quantum sub-exponential hardness of the Learning with Errors ($\mathsf{LWE}$) problem. Prior to this work, such a compiler for $\mathsf{MIP}^{*}$ was given by Kalai, Lombardi, Vaikuntanathan and Yang (STOC 2022), but the post-quantum soundness of this compiler is still under investigation.
More generally, our compiler can be applied to any $\mathsf{QIP}$ protocol which is sound only against semi-malicious provers that follow the prescribed protocol, but with possibly malicious initial state. Our compiler consists of two steps. We first show that if a language $\mathcal{L}$ has a $\mathsf{QIP}$ with semi-malicious soundness, where the prover runs in time $T$, then $\mathcal{L} \in \mathsf{QMATIME}(T)$. Then we construct a succinct classical argument for any such language, where the communication complexity grows polylogarithmically with $T$, under the post-quantum sub-exponential hardness of $\mathsf{LWE}$.
Note: After this work was finished, an independent and concurrent work (Baroni et al. 2025) resolved the question of quantum soundness of the KLVY compiler. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compiling Any $\mathsf{MIP}^{*}$ into a (Succinct) Classical Interactive Argument Huang, Andrew Kalai, Yael Tauman Quantum Physics Cryptography and Security We present a generic compiler that converts any $\mathsf{MIP}^{*}$ protocol into a succinct interactive argument where the communication and the verifier are classical, and where post-quantum soundness relies on the post-quantum sub-exponential hardness of the Learning with Errors ($\mathsf{LWE}$) problem. Prior to this work, such a compiler for $\mathsf{MIP}^{*}$ was given by Kalai, Lombardi, Vaikuntanathan and Yang (STOC 2022), but the post-quantum soundness of this compiler is still under investigation. More generally, our compiler can be applied to any $\mathsf{QIP}$ protocol which is sound only against semi-malicious provers that follow the prescribed protocol, but with possibly malicious initial state. Our compiler consists of two steps. We first show that if a language $\mathcal{L}$ has a $\mathsf{QIP}$ with semi-malicious soundness, where the prover runs in time $T$, then $\mathcal{L} \in \mathsf{QMATIME}(T)$. Then we construct a succinct classical argument for any such language, where the communication complexity grows polylogarithmically with $T$, under the post-quantum sub-exponential hardness of $\mathsf{LWE}$. Note: After this work was finished, an independent and concurrent work (Baroni et al. 2025) resolved the question of quantum soundness of the KLVY compiler. |
| title | Compiling Any $\mathsf{MIP}^{*}$ into a (Succinct) Classical Interactive Argument |
| topic | Quantum Physics Cryptography and Security |
| url | https://arxiv.org/abs/2510.08495 |