Single-Shuffle Full-Open Card-Based Protocols for Any Function
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911220910522368 |
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| author | Eriguchi, Reo Shinagawa, Kazumasa |
| author_facet | Eriguchi, Reo Shinagawa, Kazumasa |
| contents | A card-based secure computation protocol is a method for $n$ parties to compute a function $f$ on their private inputs $(x_1,\ldots,x_n)$ using physical playing cards, in such a way that the suits of revealed cards leak no information beyond the value of $f(x_1,\ldots,x_n)$. A \textit{single-shuffle full-open} protocol is a minimal model of card-based secure computation in which, after the parties place face-down cards representing their inputs, a single shuffle operation is performed and then all cards are opened to derive the output. Despite the simplicity of this model, the class of functions known to admit single-shuffle full-open protocols has been limited to a few small examples. In this work, we prove for the first time that every function admits a single-shuffle full-open protocol. We present two constructions that offer a trade-off between the number of cards and the complexity of the shuffle operation. These feasibility results are derived from a novel connection between single-shuffle full-open protocols and a cryptographic primitive known as \textit{Private Simultaneous Messages} protocols, which has rarely been studied in the context of card-based cryptography. We also present variants of single-shuffle protocols in which only a subset of cards are revealed. These protocols reduce the complexity of the shuffle operation compared to existing protocols in the same setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_17308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Single-Shuffle Full-Open Card-Based Protocols for Any Function Eriguchi, Reo Shinagawa, Kazumasa Cryptography and Security A card-based secure computation protocol is a method for $n$ parties to compute a function $f$ on their private inputs $(x_1,\ldots,x_n)$ using physical playing cards, in such a way that the suits of revealed cards leak no information beyond the value of $f(x_1,\ldots,x_n)$. A \textit{single-shuffle full-open} protocol is a minimal model of card-based secure computation in which, after the parties place face-down cards representing their inputs, a single shuffle operation is performed and then all cards are opened to derive the output. Despite the simplicity of this model, the class of functions known to admit single-shuffle full-open protocols has been limited to a few small examples. In this work, we prove for the first time that every function admits a single-shuffle full-open protocol. We present two constructions that offer a trade-off between the number of cards and the complexity of the shuffle operation. These feasibility results are derived from a novel connection between single-shuffle full-open protocols and a cryptographic primitive known as \textit{Private Simultaneous Messages} protocols, which has rarely been studied in the context of card-based cryptography. We also present variants of single-shuffle protocols in which only a subset of cards are revealed. These protocols reduce the complexity of the shuffle operation compared to existing protocols in the same setting. |
| title | Single-Shuffle Full-Open Card-Based Protocols for Any Function |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2510.17308 |