Journal of Mathematical Cryptology
Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran
Editorial Board Member: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti
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Factor-4 and 6 compression of cyclotomic subgroups of and
1Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. E-mail: (email)
Citation Information: Journal of Mathematical Cryptology. Volume 4, Issue 1, Pages 1–42, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: 10.1515/jmc.2010.001, July 2010
- Published Online:
Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields 𝔽2 m and 𝔽3 m, respectively, have been used to implement pairing-based cryptographic protocols. The pairing values lie in certain prime-order subgroups of the cyclotomic subgroups of orders 22m + 1 and 32m – 3m + 1, respectively, of the multiplicative groups and . It was previously known how to compress the pairing values over characteristic two fields by a factor of 2, and the pairing values over characteristic three fields by a factor of 6. In this paper, we show how the pairing values over characteristic two fields can be compressed by a factor of 4. Moreover, we present and compare several algorithms for performing exponentiation in the prime-order subgroups using the compressed representations. In particular, in the case where the base is fixed, we expect to gain at least a 54% speed up over the fastest previously known exponentiation algorithm that uses factor-6 compressed representations.
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