An alternate decomposition of an integer for faster point multiplication on certain elliptic curves

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2274, Issue , 2002, Pages 323-334

  Park, Young Ho ^a   Jeong, Sangtae ^b   Kim, Chang Han ^c   Lim, Jongin ^a  

^a Korea University   (South Korea)

^b Seoul National University   (South Korea)

^c Semyung University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; NUMBER THEORY; PUBLIC KEY CRYPTOGRAPHY;

COMPUTATIONAL IMPLEMENTATIONS; ELLIPTIC CURVE; ENDOMORPHISM RING; EUCLIDIAN ALGORITHMS; POINT MULTIPLICATION; SCALAR MULTIPLICATION; THEORETICAL BOUNDS;

GEOMETRY;

EID: 84958961275     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45664-3_23     Document Type: Conference Paper

References (14)

1. Ian Blake, Gadiel Seroussi and Nigel Smart, ‘Elliptic Curves in Cryptography’, London Mathematical Society Lecture Note Series. 265, Cambridge University Press, (1999).
2. G. Cornacchia, “Su di un metodo per la risoluzione in numeri interi dell’ equazione, Giornale di Matematiche di Battaglini, 46, (1908), 33-90.
3. R. Gallant, R. Lambert and S. Vanstone, “Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms”, Advances in Cryptology-Crypto 2001, LNCS 2139, Springer-Verlag (2001), 190-200.
4. K. Ireland and M. Rosen,’A classical introduction to modern number theory’, Graduate Texts in Mathematics, vol 84, Springer-Verlag, (1982).
5. N. Koblitz, “CM-curves with good cryptographic properties”, Advances in Cryptology-Crypto’91, LNCS 576, Springer-Verlag (1992), 279-287.
6. V. Müller,“Fast multiplication in elliptic curves over small fields of characteristic two”, Journal of Cryptology, 11(1998), 219-234.
7. W. Meier and O. Staffelbach, “Efficient multiplication on certain nonsupersingular elliptic curves”, Advances in Cryptology-Crypto’92, Springer-Verlag (1992), 333-344.
8. S. Pohlig, M. Hellman, An improved algorithm for computing logarithms over GF(p) its cryptographic significance,”, IEEE Trans. Inform. Theory, 24(1978), 106-110.
9. D. Shanks, “Five number theoretic algorithms” In Proc. 2nd Manitoba Conference on Numerical Mathematics (1972), 51-70.
10. B. Vallée,Une approche géométrique des algorithmes de réduction des réseaux en petite dimension”, (1986) Thése, Université de Caen.
11. N. Smart, “Elliptic curve cryptosystems over small fields of odd characteristic “, Journal of Cryptology, 12(1999), 141-145.
12. J. Solinas, “An improved algorithm for arithmetic on a familyof elliptic curves”, Advances in Cryptology-Crypto’97, LNCS 1294, Springer-Verlag (1997), 357-371.
13. J. Solinas, “Efficient arithmetic on Koblitz curves”, Design, Codes and Cryptography, 19(2000), 195-249.
14. I. Stewart and D. Tall,’Algebraic Number Theory’, Chapman and Hall, Halsted Press, (1979).