Compressed XTR

Authors:
Masaaki Shirase;Dong-Guk Han;Yasushi Hibino;Ho Won Kim;Tsuyoshi Takagi
Affiliations:
Future University-Hakodate, Japan;Electronics and Telecommunications Research Institute(ETRI), Korea;Japan Advanced Institute of Science and Technology(JAIST), Japan;Electronics and Telecommunications Research Institute(ETRI), Korea;Future University-Hakodate, Japan
Venue:
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Year:
2007

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Abstract

XTR public key system was introduced at Crypto 2000, which is based on a method to present elements of a subgroup of a multiplicative group of a finite field. Its application in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security. It was shown how the use of finite extension fields and subgroups can be combined in such a way that the number of bits to be exchanged is reduced by a factor 3.In this paper we show how to more compress the communication overhead. The compressed XTR leads to a factor 6 reduction in the representation size compared to the traditional representation and achieves as twice compactness as XTR. The computational overhead of it is a little worse than that of XTR, however the compressed XTR requires only about additional 6% computational effort. If finding 4-th roots of unity is pre-computed, then the computational overhead is only 1% compared to that of original XTR. Furthermore, the required size of public key data of it reduces about 26% from that of XTR.