Efficient Tate pairing computation using double-base chains

Pairing-based cryptosystems have developed very fast in the last few years. The efficiencies of these cryptosystems depend on the computation of the bilinear pairings. In this paper, a new efficient algorithm based on double-base chains for computing the Tate pairing is proposed for odd characteristicp > 3. The inherent sparseness of double-base number system reduces the computational cost for computing the Tate pairing evidently. The new algorithm is 9% faster than the previous fastest method for the embedding degree k = 6.

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

[2]  Iwan M. Duursma,et al.  Tate Pairing Implementation for Hyperelliptic Curves y2 = xp-x + d , 2003, ASIACRYPT.

[3]  Steven D. Galbraith,et al.  Implementing the Tate Pairing , 2002, ANTS.

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

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

[6]  Marc Joye,et al.  Trading Inversions for Multiplications in Elliptic Curve Cryptography , 2006, Des. Codes Cryptogr..

[7]  Dan Boneh,et al.  Secure Identity Based Encryption Without Random Oracles , 2004, CRYPTO.

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

[9]  Reihaneh Safavi-Naini,et al.  An Efficient Signature Scheme from Bilinear Pairings and Its Applications , 2004, Public Key Cryptography.

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

[11]  Laurent Imbert,et al.  Efficient and Secure Elliptic Curve Point Multiplication Using Double-Base Chains , 2005, ASIACRYPT.

[12]  Douglas R. Stinson,et al.  On the low hamming weight discrete logarithm problem for nonadjacent representations , 2005, Applicable Algebra in Engineering, Communication and Computing.

[13]  Colin Boyd,et al.  Advances in Cryptology - ASIACRYPT 2001 , 2001 .

[14]  Tsuyoshi Takagi,et al.  Efficient Computations of the Tate Pairingfor the Large MOV Degrees , 2002, ICISC.

[15]  Brent Waters,et al.  Efficient Identity-Based Encryption Without Random Oracles , 2005, EUROCRYPT.

[16]  Tomio Hirata,et al.  Refined Computations for Points of the Form 2kP Based on Montgomery Trick , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[17]  Antoine Joux.  A One Round Protocol for Tripartite Diffie-Hellman , 2000, ANTS.

[18]  T. Hirata,et al.  LETTER Refined Computations for Points of the Form 2 k P Based on , 2006 .

[19]  Hideki Imai,et al.  Efficient Algorithms for Tate Pairing , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[20]  Kristin E. Lauter,et al.  Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation , 2003, CT-RSA.

[21]  Alfred Menezes,et al.  Reducing elliptic curve logarithms to logarithms in a finite field , 1993, IEEE Trans. Inf. Theory.

[22]  Hovav Shacham,et al.  Short Signatures from the Weil Pairing , 2001, J. Cryptol..

[23]  P. L. Montgomery.  Speeding the Pollard and elliptic curve methods of factorization , 1987 .

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

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

[26]  Ian F. Blake,et al.  Refinements of Miller's algorithm for computing the Weil/Tate pairing , 2006, J. Algorithms.

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

[28]  Antoine Joux,et al.  A One Round Protocol for Tripartite Diffie–Hellman , 2000, Journal of Cryptology.

[29]  Dan Boneh,et al.  Short Signatures Without Random Oracles , 2004, EUROCRYPT.

[30]  Hovav Shacham,et al.  Short Group Signatures , 2004, CRYPTO.