TY - GEN

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

AU - Kamata, Sei Ichiro

PY - 2011/12/1

Y1 - 2011/12/1

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

T3 - Proceedings of the 2011 7th International Conference on Information Assurance and Security, IAS 2011

SP - 275

EP - 279

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

T2 - 2011 7th International Conference on Information Assurance and Security, IAS 2011

Y2 - 5 December 2011 through 8 December 2011

ER -