### Abstract

We introduce a problem of distinguishing between two quantum states as a new underlying problem to build a computational cryptographic scheme that is "secure" against quantum adversary. Our problem is a natural generalization of the distinguishability problem between two probability distributions, which are commonly used in computational cryptography. More precisely, our problem QSCD_{ff} is the computational distinguishability problem between two types of random coset states with a hidden permutation over the symmetric group. We show that (i) QSCD_{ff} has the trapdoor property; (ii) the average-case hardness of QSCD_{ff} coincides with its worst-case hardness; and (iii) QSCD_{ff} is at least as hard in the worst case as the graph automorphism problem. Moreover, we show that QSCD_{ff} cannot be efficiently solved by any quantum algorithm that naturally extends Shor's factorization algorithm. These cryptographic properties of QSCD_{ff} enable us to construct a public-key cryptosystem, which is likely to withstand any attack of a polynomial-time quantum adversary.

Original language | English |
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Pages (from-to) | 268-284 |

Number of pages | 17 |

Journal | LECTURE NOTES IN COMPUTER SCIENCE |

Volume | 3494 |

DOIs | |

Publication status | Published - 2005 |

Externally published | Yes |

Event | 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology - EUROCRYPT 2005 - Aarhus, Denmark Duration: 2005 May 22 → 2005 May 26 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*LECTURE NOTES IN COMPUTER SCIENCE*,

*3494*, 268-284. https://doi.org/10.1007/11426639_16