## Abstract

Secure computation enables a number of players each holding a secret input value to compute a function of the inputs without revealing the inputs. It is known that secure computation is possible physically when the inputs are given as a sequence of physical cards. This research area is called card-based cryptography. One of the important problems in card-based cryptography is to minimize the number of cards and shuffles, where a shuffle is the most important (and somewhat heavy) operation in card-based protocols. In this paper, we determine the minimum number of shuffles for achieving general secure computation. Somewhat surprisingly, the answer is just one, i.e., we design a protocol which securely computes any Boolean circuit with only a single shuffle. The number of cards required for our protocol is proportional to the size of the circuit to be computed.

Original language | English |
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Pages (from-to) | 248-261 |

Number of pages | 14 |

Journal | Discrete Applied Mathematics |

Volume | 289 |

DOIs | |

Publication status | Published - Jan 31 2021 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics