### Abstract

It is shown that public key cryptosystems based on discrete logarithm probrem can be solved if the quantum computer and Shor's algorithm are realized. Thus a new cryptosystem called post-quantum cryptosystem so as not to be broken by quantum computer is needed. NTRU is proposed by Hoffstein et al. in 1998. It is one of post-quantum cryptosystem. It is based on problems on lattice for which there are no efficient algorithms to solve. In NTRU, using convolution polynomial ring as Z_{q}[X]/(X^{n}-1). However, (X-1), that is a trivial factor of X^{n}-1 sometimes make problems. Thus we consider a variant using a quotient polynomial ring such as Z_{q}[X]/(X^{n} + X^{x-1} +^{...}+X + 1) and CVMA: Cyclic Vector Multiplication Algorithm.

Original language | English |
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Title of host publication | 2015 IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 384-385 |

Number of pages | 2 |

ISBN (Print) | 9781479987443 |

DOIs | |

Publication status | Published - Aug 20 2015 |

Event | 2nd IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015 - Taipei, Taiwan, Province of China Duration: Jun 6 2015 → Jun 8 2015 |

### Other

Other | 2nd IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015 |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 6/6/15 → 6/8/15 |

### Fingerprint

### Keywords

- Bismuth

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Networks and Communications
- Electrical and Electronic Engineering
- Instrumentation
- Media Technology

### Cite this

*2015 IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015*(pp. 384-385). [7216956] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICCE-TW.2015.7216956

**Efficient implimentation of NTRU over all one polynomial ring with CVMA.** / Misumi, Koki; Nogami, Yasuyuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2015 IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015.*, 7216956, Institute of Electrical and Electronics Engineers Inc., pp. 384-385, 2nd IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015, Taipei, Taiwan, Province of China, 6/6/15. https://doi.org/10.1109/ICCE-TW.2015.7216956

}

TY - GEN

T1 - Efficient implimentation of NTRU over all one polynomial ring with CVMA

AU - Misumi, Koki

AU - Nogami, Yasuyuki

PY - 2015/8/20

Y1 - 2015/8/20

N2 - It is shown that public key cryptosystems based on discrete logarithm probrem can be solved if the quantum computer and Shor's algorithm are realized. Thus a new cryptosystem called post-quantum cryptosystem so as not to be broken by quantum computer is needed. NTRU is proposed by Hoffstein et al. in 1998. It is one of post-quantum cryptosystem. It is based on problems on lattice for which there are no efficient algorithms to solve. In NTRU, using convolution polynomial ring as Zq[X]/(Xn-1). However, (X-1), that is a trivial factor of Xn-1 sometimes make problems. Thus we consider a variant using a quotient polynomial ring such as Zq[X]/(Xn + Xx-1 +...+X + 1) and CVMA: Cyclic Vector Multiplication Algorithm.

AB - It is shown that public key cryptosystems based on discrete logarithm probrem can be solved if the quantum computer and Shor's algorithm are realized. Thus a new cryptosystem called post-quantum cryptosystem so as not to be broken by quantum computer is needed. NTRU is proposed by Hoffstein et al. in 1998. It is one of post-quantum cryptosystem. It is based on problems on lattice for which there are no efficient algorithms to solve. In NTRU, using convolution polynomial ring as Zq[X]/(Xn-1). However, (X-1), that is a trivial factor of Xn-1 sometimes make problems. Thus we consider a variant using a quotient polynomial ring such as Zq[X]/(Xn + Xx-1 +...+X + 1) and CVMA: Cyclic Vector Multiplication Algorithm.

KW - Bismuth

UR - http://www.scopus.com/inward/record.url?scp=84959543294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959543294&partnerID=8YFLogxK

U2 - 10.1109/ICCE-TW.2015.7216956

DO - 10.1109/ICCE-TW.2015.7216956

M3 - Conference contribution

AN - SCOPUS:84959543294

SN - 9781479987443

SP - 384

EP - 385

BT - 2015 IEEE International Conference on Consumer Electronics - Taiwan, ICCE-TW 2015

PB - Institute of Electrical and Electronics Engineers Inc.

ER -