### Abstract

We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem, QSCD _{ff}, is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show that QSCD _{ff} has three properties of cryptographic interest: (i) QSCD _{ff} has a trapdoor; (ii) the average-case hardness of QSCD _{ff} coincides with its worst-case hardness; and (iii) QSCD _{ff} is computationally at least as hard as the graph automorphism problem in the worst case. These cryptographic properties enable us to construct a quantum public-key cryptosys-tem which is likely to withstand any chosen plaintext attack of a polynomial-time quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies on similar cryptographic properties of QSCDcyc.

Original language | English |
---|---|

Pages (from-to) | 528-555 |

Number of pages | 28 |

Journal | Journal of Cryptology |

Volume | 25 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 Jul |

Externally published | Yes |

### Fingerprint

### Keywords

- Computational indistinguishability
- Graph automorphism problem
- Quantum cryptography
- Quantum publickey cryptosystem
- Trapdoor
- Worst-case/average-case equivalence

### ASJC Scopus subject areas

- Software
- Computer Science Applications
- Applied Mathematics

### Cite this

*Journal of Cryptology*,

*25*(3), 528-555. https://doi.org/10.1007/s00145-011-9103-4

**Computational indistinguishability between quantum states and its cryptographic application.** / Kawachi, Akinori; Koshiba, Takeshi; Nishimura, Harumichi; Yamakami, Tomoyuki.

Research output: Contribution to journal › Article

*Journal of Cryptology*, vol. 25, no. 3, pp. 528-555. https://doi.org/10.1007/s00145-011-9103-4

}

TY - JOUR

T1 - Computational indistinguishability between quantum states and its cryptographic application

AU - Kawachi, Akinori

AU - Koshiba, Takeshi

AU - Nishimura, Harumichi

AU - Yamakami, Tomoyuki

PY - 2012/7

Y1 - 2012/7

N2 - We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem, QSCD ff, is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show that QSCD ff has three properties of cryptographic interest: (i) QSCD ff has a trapdoor; (ii) the average-case hardness of QSCD ff coincides with its worst-case hardness; and (iii) QSCD ff is computationally at least as hard as the graph automorphism problem in the worst case. These cryptographic properties enable us to construct a quantum public-key cryptosys-tem which is likely to withstand any chosen plaintext attack of a polynomial-time quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies on similar cryptographic properties of QSCDcyc.

AB - We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem, QSCD ff, is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show that QSCD ff has three properties of cryptographic interest: (i) QSCD ff has a trapdoor; (ii) the average-case hardness of QSCD ff coincides with its worst-case hardness; and (iii) QSCD ff is computationally at least as hard as the graph automorphism problem in the worst case. These cryptographic properties enable us to construct a quantum public-key cryptosys-tem which is likely to withstand any chosen plaintext attack of a polynomial-time quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies on similar cryptographic properties of QSCDcyc.

KW - Computational indistinguishability

KW - Graph automorphism problem

KW - Quantum cryptography

KW - Quantum publickey cryptosystem

KW - Trapdoor

KW - Worst-case/average-case equivalence

UR - http://www.scopus.com/inward/record.url?scp=84865243375&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865243375&partnerID=8YFLogxK

U2 - 10.1007/s00145-011-9103-4

DO - 10.1007/s00145-011-9103-4

M3 - Article

VL - 25

SP - 528

EP - 555

JO - Journal of Cryptology

JF - Journal of Cryptology

SN - 0933-2790

IS - 3

ER -