### Abstract

There are a lot of previous works on common key encryptions such as DES, AES, etc, In this paper, a new common key encryption algorithm is proposed using Hilbert curves which are a one-to-one mapping between N-dimensional (N-D) spaces and 1-D space (a line). This is based on a property having a sharp rise in the number of Hilbert curve patterns in N-D spaces. In the case of N = 2, there are only four patterns, while if N is 5, the number of the patterns is more than 1 billions. Operations of addition and multiplication are denned on a curve, based on a mapping of a point in N-D spaces to a point on a line. In order to realize a cryptosystem, the algorithm utilizes Hilbert ordered point addresses, which is expressed as the coordinates of the points in N-dimensional space.

Original language | English |
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Title of host publication | Proceedings of the 2011 7th International Conference on Information Assurance and Security, IAS 2011 |

Pages | 275-279 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2011 |

Event | 2011 7th International Conference on Information Assurance and Security, IAS 2011 - Malacca Duration: 2011 Dec 5 → 2011 Dec 8 |

### Other

Other | 2011 7th International Conference on Information Assurance and Security, IAS 2011 |
---|---|

City | Malacca |

Period | 11/12/5 → 11/12/8 |

### Fingerprint

### Keywords

- Common Key Encryption
- Hilbert curve
- Space-filling curve
- Symmetric Key Cipher

### ASJC Scopus subject areas

- Information Systems
- Safety, Risk, Reliability and Quality

### Cite this

*Proceedings of the 2011 7th International Conference on Information Assurance and Security, IAS 2011*(pp. 275-279). [6122832] https://doi.org/10.1109/ISIAS.2011.6122832

**A common key encryption algorithm using N-dimensional Hilbert curves.** / Kamata, Seiichiro.

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

*Proceedings of the 2011 7th International Conference on Information Assurance and Security, IAS 2011.*, 6122832, pp. 275-279, 2011 7th International Conference on Information Assurance and Security, IAS 2011, Malacca, 11/12/5. https://doi.org/10.1109/ISIAS.2011.6122832

}

TY - GEN

T1 - A common key encryption algorithm using N-dimensional Hilbert curves

AU - Kamata, Seiichiro

PY - 2011

Y1 - 2011

N2 - There are a lot of previous works on common key encryptions such as DES, AES, etc, In this paper, a new common key encryption algorithm is proposed using Hilbert curves which are a one-to-one mapping between N-dimensional (N-D) spaces and 1-D space (a line). This is based on a property having a sharp rise in the number of Hilbert curve patterns in N-D spaces. In the case of N = 2, there are only four patterns, while if N is 5, the number of the patterns is more than 1 billions. Operations of addition and multiplication are denned on a curve, based on a mapping of a point in N-D spaces to a point on a line. In order to realize a cryptosystem, the algorithm utilizes Hilbert ordered point addresses, which is expressed as the coordinates of the points in N-dimensional space.

AB - There are a lot of previous works on common key encryptions such as DES, AES, etc, In this paper, a new common key encryption algorithm is proposed using Hilbert curves which are a one-to-one mapping between N-dimensional (N-D) spaces and 1-D space (a line). This is based on a property having a sharp rise in the number of Hilbert curve patterns in N-D spaces. In the case of N = 2, there are only four patterns, while if N is 5, the number of the patterns is more than 1 billions. Operations of addition and multiplication are denned on a curve, based on a mapping of a point in N-D spaces to a point on a line. In order to realize a cryptosystem, the algorithm utilizes Hilbert ordered point addresses, which is expressed as the coordinates of the points in N-dimensional space.

KW - Common Key Encryption

KW - Hilbert curve

KW - Space-filling curve

KW - Symmetric Key Cipher

UR - http://www.scopus.com/inward/record.url?scp=84856643508&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856643508&partnerID=8YFLogxK

U2 - 10.1109/ISIAS.2011.6122832

DO - 10.1109/ISIAS.2011.6122832

M3 - Conference contribution

AN - SCOPUS:84856643508

SN - 9781457721533

SP - 275

EP - 279

BT - Proceedings of the 2011 7th International Conference on Information Assurance and Security, IAS 2011

ER -