Improved Implementations of Cryptosystems Based on Tate Pairing

Hu et al . first studied pairing computations on supersingular elliptic curve with odd embedding degree k = 3 and applied them to Identity-based cryptosystems. In this paper, a careful analysis of the pairing computation on this family of supersingular curves is given. Some novel improvements are presented from different points of view and hence speed up the implementation of Identity-based cryptosystems.

[1]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[2]  Eric R. Verheul,et al.  Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems , 2001, EUROCRYPT.

[3]  G. Frey,et al.  A remark concerning m -divisibility and the discrete logarithm in the divisor class group of curves , 1994 .

[4]  Atsuko Miyaji,et al.  Efficient Elliptic Curve Exponentiation Using Mixed Coordinates , 1998, ASIACRYPT.

[5]  M. Anwar Hasan,et al.  Asymmetric Squaring Formulae , 2007, 18th IEEE Symposium on Computer Arithmetic (ARITH '07).

[6]  Joseph H. Silverman,et al.  The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[7]  Moti Yung,et al.  Advances in Cryptology — CRYPTO 2002 , 2002, Lecture Notes in Computer Science.

[8]  Paulo S. L. M. Barreto,et al.  Efficient pairing computation on supersingular Abelian varieties , 2007, IACR Cryptol. ePrint Arch..

[9]  Jiwu Huang,et al.  A note on the Ate pairing , 2008, International Journal of Information Security.

[10]  S. Galbraith,et al.  Advances in Elliptic Curve Cryptography: Pairings , 2005 .

[11]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[12]  Paulo S. L. M. Barreto,et al.  Efficient Algorithms for Pairing-Based Cryptosystems , 2002, CRYPTO.

[13]  Hu Lei.  Compression of Tate Pairings on Elliptic Curves , 2007 .

[14]  Hyang-Sook Lee,et al.  Efficient and Generalized Pairing Computation on Abelian Varieties , 2009, IEEE Transactions on Information Theory.

[15]  Frederik Vercauteren,et al.  The Eta Pairing Revisited , 2006, IEEE Transactions on Information Theory.

[16]  Kazuo Ohta,et al.  Advances in Cryptology — ASIACRYPT’98 , 2002, Lecture Notes in Computer Science.

[17]  Colin Boyd,et al.  Cryptography and Coding , 1995, Lecture Notes in Computer Science.

[18]  Eiji Okamoto,et al.  Optimised Versions of the Ate and Twisted Ate Pairings , 2007, IMACC.

[19]  Lei Hu,et al.  Implementation of Cryptosystems Based on Tate Pairing , 2005, Journal of Computer Science and Technology.

[20]  Ian F. Blake,et al.  Elliptic curves in cryptography , 1999 .