Montgomery scalar multiplication for genus 2 curves

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

Volumn 3076, Issue , 2004, Pages 153-168

  Duquesne, Sylvain ^a  

^a UNIV MONTPELLIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOGRAPHY; NUMBER THEORY; SMART CARDS;

ELLIPTIC CURVE; GENUS 2 CURVES; HYPER-ELLIPTIC CURVES; JACOBIANS; MONTGOMERY; SCALAR MULTIPLICATION;

GEOMETRY;

EID: 21144448858     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24847-7_11     Document Type: Article

References (28)

1. Brier, E., Joye, M.: Weierstrass Elliptic Curves and Side-Channel Attacks, Public Key Cryptography, Lecture Notes in Computer Science, 2274 (2002)
2. Cantor, D. G.: Computing on the Jacobian of a hyperelliptic curve. Math. Comp., 48 (1987) 95-101
3. Cassel, J. W. S., Flynn, E. V.: Prolegomena to a middlebrow arithmetic of curves of genus 2, London Mathematical Society Lecture Note Series, 230 (1996)
4. Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates, Asiacrypt'98, Lecture Notes in Computer Science, 1514 (1998) 51-65
5. Coron, J. S.: Resistance against differential power analysis for elliptic curve cryptosystems, CHES'99, Lecture Notes in Computer Science, 1717 (1999) 292-302
6. Doche, C., Duquesne, S.: Manual for the elliptic curve library, Arehcc report (2003)
7. p, preprint (2003)
8. Flynn, E. V.: The group law on the Jacobian of a curve of genus 2, J. reine angew. Math., 439 (1993), 45-69
9. Flynn, E. V.: ftp site, ftp://ftp.liv.ac.uk/pub/genus2/kummer
10. p hedged against Non-Differential Side-Channel Attacks, preprint
11. Gaudry, P., Schost, E.: Construction of secure random curves of genus 2 over prime fields, Eurocrypt'04, Lecture Notes in Computer Science (2004)
12. Harley, R.: Fast arithmetic on genus 2 curves, available at http://cristal.inria.fr/∼harley/hyper (2000)
13. Izu, T., Takagi, T.: A fast Elliptic Curve Multiplication Resistant against Side Channel Attacks, preprint
14. Koblitz, N.: Elliptic curve cryptosystems, Math. Comp., 48 (1987) 203-209
15. Koblitz, N.: Algebraic aspects of cryptography, Algorithms and Computation in Mathematics, 3 (1998)
16. Kocher, P. C.: Timing attacks on implementations of DH, RSA, DSS and other systems, CRYPTO'96, Lecture Notes in Computer Science, 1109 (1996), 104-113
17. Kocher, P. C., Jaffe, J., Jun, B.: Differential power analysis, CRYPTO'99, Lecture Notes in Computer Science, 1666 (1999) 388-397
18. Koyama, K., Tsuruoka, Y.: Speeding up elliptic cryptosystems by using a signed binary window method, Crypto'92, Lecture Notes in Computer Science, 740 (1993) 345-357
19. Lange, T.: Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae, Cryptology ePrint Archive, 121 (2002)
20. Lange, T.: Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves, Cryptology ePrint Archive, 147 (2002)
21. Lange, T.: Weighted Coordinates on Genus 2 Hyperelliptic Curves, Cryptology ePrint Archive, 153 (2002)
22. Matsuo, K. Chao, J. Tsujii, S.: An improved baby step giant step algorithm for point counting of hyperelliptic curves over finite fields, ANTS-V, Lecture Notes in Computer Science, 2369 (2002) 461-474
23. Miller, V. S.: Use of elliptic curves in cryptography, Crypto'85, Lecture Notes in Computer Science, 218 (1986) 417-426
24. Montgomery, P. L.: Speeding the Pollard and elliptic curve methods of factorization, Math. Comp., 48 (1987) 243-164
25. Mumford, D.: Tata lectures on Theta II, Birkhäuser (1984)
26. Okeya, K., Kurumatani, H., Sakurai, K.: Elliptic curves with the Montgomery-form and their cryptographic applications, Public Key Cryptography, Lecture Notes in Computer Science, 1751 (2000) 238-257
27. Okeya, O., Sakurai, K.: Efficient Elliptic Curve Cryptosystems from a Scalar Multiplication Algorithm with Recovery of the y-Coordinate on a Montgomery-Form Elliptic Curve, Cryptographic Hardware and Embedded Systems, Lecture Notes in Computer Science, 2162 (2001) 126-141
28. Quisquater, J. J., Samyde, D.: ElectroMagnetic Analysis (EMA): Measures and Countermeasures for Smart Cards, e-smart 2001, Lecture Notes in Computer Science, 2140, (2001), 200-210