Simple power analysis on fast modular reduction with NIST recommended elliptic curves

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

Volumn 3783 LNCS, Issue , 2005, Pages 169-180

  Sakai, Yasuyuki ^a   Sakurai, Kouichi ^b  

^a MITSUBISHI ELECTRIC CORPORATION   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

Author keywords

Elliptic curve cryptosystem; Generalized mersenne prime; Modular reduction; Side channel analysis; Unified code

Indexed keywords

CODES (STANDARDS); CRYPTOGRAPHY;

ELLIPTIC CURVE CRYPTOSYSTEM; GENERALIZED MERSENNE PRIME; MODULAR REDUCTION; SIDE CHANNEL ANALYSIS; UNIFIED CODE;

INFORMATION MANAGEMENT;

EID: 33646741773     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11602897_15     Document Type: Conference Paper

References (18)

1. J.F. Dhem, F. Koeune, P.A. Leroux, P. Mestré and J.-J. Quisquater, "A practical implementation of the timing attack," CARDIS 1998, LNCS 1820, pp.175-190, Springer-Verlag, 1998.
2. "Digital signature standard (DSS)," FTPS PUB 186-2, U.S. National Institute of Standards and Technology, 2000.
3. E. Brier and M. Joye, "Weierstrass elliptic curves and side-channel attacks," Public Key Cryptography - PKC 2002, LNCS 2274, pp.335-345, Springer-Verlag, 2002.
4. M. Brown, D. Hankerson, J. Lopez and A. Menezes, "Software implementation of the NIST elliptic curves over prime fields," Technical Report CORK 2000-56, University of Waterloo, 2000.
5. J.-S. Coron, "Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems," Cryptographic Hardware and Embedded Systems - CHES'99, LNCS 1717, pp.292-302, Springer-Verlag, 1999.
6. C. Gebotys and R. Gebotys, "Secure elliptic curve implementations: an analysis of resistance to power-attacks in a DSP processor," Cryptographic Hardware and Embedded Systems - CHES 2002, LNCS 2523, pp. 114-128, Springer-Verlag, 2002.
7. G. Hachez and J.-J. Quisquater, "Montgomery exponentiation with no final subtractions: Improved Results," Cryptographic Hardware and Embedded Systems-CHES 2000, LNCS 1965, pp.293-301. Springer-Verlag, 2000.
8. M. Joye and J.-J. Quisquater, "Hessian elliptic curves and side channel attacks," Cryptographic Hardware and Embedded Systems - CHES 2001, LNCS 2162, pp.402-410, Springer-Verlag, 2001.
9. P.C. Kocher, "Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems," Advances in Cryptology - CRYPTO '96, LNCS 1109, pp.104-113, Springer-Verlag, 1996.
10. P.-Y. Liardet and N.P. Smart, "Preventing SPA/DPA in ECC systems using the Jacobi form," Cryptographic Hardware and Embedded Systems - CHES 2001, LNCS 2162, pp.391-401, Springer-Verlag, 2001.
11. A.J. Menezes, P.C. van Oorschot and S.A. Vanstone, "Handbook of applied cryptography," CRC Press, 1966.
12. P.L. Montgomery, "Modular multiplication without trial division," Mathematics of Computation, vol. 44, no. 170, pp.519-521, 1885.
13. W. Schindler, "A timing attack against RSA with the Chinese Remainder Theorem," Cryptographic Hardware and Embedded Systems - CHES 2000, LNCS 1965, pp.109-124, Springer-Verlag, 2000.
14. Certicom, "Standard for efficient cryptography, SEC2: Recommended elliptic domain parameters," 2000.
15. J.A. Solinas, "Generalized Mersenne numbers," Technical Report CORR 99-39, University of Waterloo, 1999.
16. C.D. Walter, "Montgomery exponentiation needs no final subtractions," Electric Letters, vol. 35, no. 21, pp.1831-1832, 1999.
17. C.D. Walter and S. Thompson, "Distinguishing exponent digits by observing modular subtractions," RSA Conference 2001, LNCS 2020, pp. 192-207, Springer-Verlag, 2001.
18. C.D. Walter, "Simple power analysis of unified code for EGG double and add," Cryptographic Hardware and Embedded System - CHES 2004, LNCS 3156, pp.191-204, Springer-Verlag, 2004.