(Virtually) free randomization techniques for elliptic curve cryptography

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

Volumn 2836, Issue , 2003, Pages 348-359

  Ciet, Mathieu ^a   Joye, Marc ^b  

^a B 1348   (Belgium)

^b GEMPLUS   (France)

Author keywords

Elliptic curve cryptography; Elliptic curve models; Implementation attacks; Point multiplication algorithms; Randomization; Side channel analysis

Indexed keywords

CRYPTOGRAPHY; PUBLIC KEY CRYPTOGRAPHY; RANDOM PROCESSES; SET THEORY; SIDE CHANNEL ATTACK;

ELLIPTIC CURVE; ELLIPTIC CURVE CRYPTOGRAPHY; IMPLEMENTATION ATTACKS; POINT MULTIPLICATION; RANDOMIZATION; SIDE-CHANNEL ANALYSIS;

GEOMETRY;

EID: 0142156711     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-39927-8_32     Document Type: Article

References (25)

1. IEEE Std 1363-2000. IEEE Standard Specifications for Public-Key Cryptography. IEEE Computer Society, August 29, 2000.
2. SECG: Standard for Efficient Cryptography Group. SEC 1: Elliptic Curve Cryptography. Certicom Research, Version 1.0, September 20, 2000. Available at URL http://www.secg.org/secg_docs.htm.
3. Ian Blake, Gadiel Seroussi, and Nigel Smart. Elliptic Curves in Cryptography, volume 265 of London Mathematical Society. Cambridge University Press, 2000.
4. Christophe Clavier and Marc Joye. Universal exponentiaion algorithm. In Ç.K. Koç, D. Naccache, and C. Paar, editors, Cryptographic Hardware and Embedded Systems - CHES 2001, volume 2162 of Lecture Notes in Computer Science, pages 300-308. Springer-Verlag, 2001.
5. Henri Cohen, Atsuko Miyaji, and Takatoshi Ono. Efficient elliptic curve using mixed coordinates. In K. Ohta and D. Pei, editors, Advances in Cryptology - ASIACRYPT'98, volume 1514 of Lecture Notes in Computer Science, pages 51-65. Springer-Verlag, 1998.
6. Jean-Sébastien Coron. Resistance against differential power analysis for elliptic curve cryptosystems. In Ç.K. Koç and C. Paar, editors, Cryptographic Hardware and Embedded Systems (CHES '99), volume 1717 of Lecture Notes in Computer Science, pages 292-302. Springer-Verlag-Verlag, 1999.
7. Erik De Win, Serge Mister, Bart Preneel, and Michael Wiener. On the performance of signature schemes based on elliptic curves. In J.-P. Buhler, editor, Algorithmic Number Theory Symposium, volume 1423 of Lecture Notes in Computer Science, pages 252-266. Springer-Verlag-Verlag, 1998.
8. Taher ElGamal. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 31(4):469-472, 1985.
9. Shuhong Gao and Hendrik W. Lenstra, Jr. Optimal normal bases. Designs, Codes and Cryptography, 2:315-323, 1992.
10. Louis Goubin. A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems. In Y. Desmedt, editor, Public Key Cryptography (PKC 2003), volume 2567 of Lecture Notes in Computer Science, pages 199-210. Springer-Verlag, 2003.
11. Darrel Hankerson, Julio López Hernandez, and Alfred Menezes. Software implementation of elliptic curve cryptography over binary fields. In Ç.K. Koç and C. Paar, editors, Cryptographic Hardware and Embedded Systems - CHES 2000, volume 1965 of Lecture Notes in Computer Science, pages 1-24. Springer-Verlag, 2000.
12. Yvonne Hitchcock and Paul Montague. A new elliptic curve scalar multiplication algorithm to resist simple power analysis. In L.M. Batten and J. Seberry, editors, Information Security and Privacy (ACISP 2002), volume 2384 of Lecture Notes in Computer Science, pages 214-225. Springer-Verlag, 2002.
13. Kouichi Itoh, Jun Yajima, Masahiko Takenaka, and Naoya Torii. DPA countermeasures by improving the window method. In B.S. Kaliski Jr., Ç.K. Koç, and C. Paar, editors, Cryptographic Hardware and Embedded Systems - CHES 2002, volume 2523 of Lecture Notes in Computer Science, pages 303-317. Springer-Verlag, 2003.
14. Marc Joye and Christophe Tymen. Protections against differential analysis for elliptic curve cryptography: An algebraic approach. In Ç.K. Koç, D. Naccache, and C. Paar, editors, Cryptographic Hardware and Embedded Systems (CHES 2001), volume 2162 of Lecture Notes in Computer Science, pages 377-390. Springer-Verlag-Verlag, 2001.
15. Neal Koblitz. CM-curves with good cryptographic properties. In J. Feigenbaum, editor, Advances in Cryptology - CRYPTO '91, volume 576 of Lecture Notes in Computer Science, pages 279-287. Springer-Verlag, 1992.
16. Paul Kocher. Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In N. Koblitz, editor, Advances in Cryptology - CRYPTO '96, volume 1109 of Lecture Notes in Computer Science, pages 104-113. Springer-Verlag, 1996.
17. Paul Kocher, Joshua Jaffe, and Benjamin Jun. Differential power analysis. In M. Wiener, editor, Advances in Cryptology - CRYPTO '99, volume 1666 of Lecture Notes in Computer Science, pages 388-397. Springer-Verlag, 1999.
18. Alfred J. Menezes. Elliptic curve public key cryptosystems. Kluwer Academic Publishers, 1993.
19. Francois Morain and Jørge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Inform. Theor. Appl, 24:531-543, 1990.
20. Katsuyuki Okeya, Kunihiko Miyazaki, and Kouichi Sakurai. A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks. In K. Kim, editor, Information and Communications Security, volume 2288 of Lecture Notes in Computer Science, pages 428-439. Springer-Verlag, 2002.
21. Katsuyuki Okeya and Kouichi Sakurai. Power analysis breaks elliptic curve cryptosystems even secure against the timing attack. In B.K. Roy and E. Okamoto, editors, Progress in Cryptology - INDOCRYPT 2000, volume 1977 of Lecture Notes in Computer Science, pages 178-190. Springer-Verlag, 2000.
22. Richard Schroeppel, Hilarie Orman, Sean W. O'Malley, and Oliver Spatscheck. Fast key exchange with elliptic curve systems. In D. Coppersmith, editor, Advances in Cryptography - CRYPTO '95, volume 963 of Lecture Notes in Computer Science, pages 43-56. Springer-Verlag, 1995.
23. Jerome A. Solinas. An improved algorithm for arithmetic on a family of elliptic curves. In B.S. Kaliski Jr., editor, Advances in Cryptology - CRYPTO '97, volume 1294 of Lecture Notes in Computer Science, pages 357-371. Springer-Verlag, 1997.
24. Jerome A. Solinas. Efficient arithmetic on Koblitz curves. Designs, Codes and Cryptography, 19:195-249, 2000.
25. Jerome A. Solinas. Low-weight binary representations for pairs of integers. Technical Report CORR 2001-41, CACR, Waterloo, 2001. Available at URL http://www.cacr.math.uwaterloo.ca/∼techreports/2001/corr2001-41.ps.