Refined computations for points of the form 2kP based on montgomery trick

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E89-A, Issue 1, 2006, Pages 334-339

  Adachi, Daisuke ^a   Hirata, Tomio ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Elliptic curve arithmetic; Montgomery trick; Scalar multiplication; Window method

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

ELLIPTIC CURVE ARITHMETIC; FIELD INVERSION; MONTGOMERY TRICK; SCALAR MULTIPLICATION; WINDOW METHOD;

COMPUTATION THEORY;

EID: 32244433688     PISSN: 09168508     EISSN: 17451337     Source Type: Journal    
DOI: 10.1093/ietfec/e89-a.1.334     Document Type: Article

References (14)

1. R.M. Avanzi, "On multi-exponentiation in cryptography," IACR Cryptology ePrint Archive, 2002, Available at, http://eprint.iacr.org/2002/154. ps.gz
2. M. Ciet, M. Joye, K. Lauter, and P.L. Montgomery, "Trading inversions for multiplications in elliptic curve cryptography," IACR Cryptology ePrint Archive, 2003, Available at, http://eprint.iacr.org/2003/257. ps.gz
3. H. Cohen, A Course in Computational Algebraic Number Theory, Graduate Texts in Math., no.138, Springer-Verlag, Berlin, 1993.
4. H. Cohen, A. Miyaji, and T. Ono, "Efficient elliptic curve exponentiation using mixed coordinates," Advances in Cryptology- ASIACRYPT'98, LNCS, vol.1514, pp.51-65, Springer-Verlag, 1998.
5. D.M. Gordon, "A survey of fast exponentiation methods," J. Algorithms, vol.27, pp. 129-146, 1998.
6. J. Guajardo and C. Paar, "Efficient algorithms for elliptic curve cryptosystems," Advances in Cryptology - Crypto'97, LNCS, vol.1294, pp.342-356, Springer-Verlag, 1997.
7. D.E. Knuth, The Art of Computer Programming, vol.2, Seminumerical Algorithms, 3rd ed., Addison-Wesley, Reading, MA, 1997.
8. K. Koyama and Y. Tsuruoka, "Speeding up elliptic cryptosystems by using a signed binary window method," Advances in Cryptology - Crypto'92, LNCS, vol.740, pp.345-357, Springer-Verlag, 1993.
9. F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol.24, no.6, pp.531-544, 1990.
10. P.L. Montgomery, "Speeding the Pollard and elliptic curve methods of factorization," Math. Comput., vol.48, pp.243-264, 1987.
11. V. Müller, "Efficient algorithms for multiplication on elliptic curves," Proc. GI-Arbeitskonferenz Chipkarten 1998, TU München, 1998.
12. NIST, Recommended elliptic curves for federal government use, 1999, Available at, http://csrc.nist.gov/encryption/dss/ecdsa/NISTReCur.pdf
13. Y. Sakai and K. Sakurai, "Efficient scalar multiplications on elliptic curves with direct computations of several doublings," IEICE Trans. Fundamentals, vol.E84-A, no.1, pp.120-129, Jan. 2001.
14. J.A. Solinas, "Efficient arithmetic on Koblitz curves," Des. Codes Cryptogr., vol.19, pp. 195-249, 2000.