Parallelizable elliptic curve point multiplication method with resistance against side-channel attacks

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

Volumn 2433, Issue , 2002, Pages 402-413

  Möller, Bodo ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; SECURITY OF DATA;

ELLIPTIC CURVE POINT MULTIPLICATIONS; INFORMATION LEAKAGE; TWO PROCESSORS;

SIDE CHANNEL ATTACK;

EID: 84945249400     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45811-5_31     Document Type: Conference Paper

References (25)

1. Bier, É., and Joye, M. Weierstraß elliptic curves and side-channel attacks. In Public Key Cryptography–PKC 2002 (2002), D. Naccache and P. Paillier, Eds., vol. 2274 of Lecture Notes in Computer Science, pp. 335–345.
2. Boneh, D., DeMillo, R. A., and Lipton, R. J. On the importance of eliminating errors in cryptographic computations. Journal of Cryptology 14 (2001), 101–119.
3. Brickell, E. F., Gordon, D. M., McCurley, K. S., and Wilson, D. B. Fast exponentiation with precomputation. In Advances in Cryptology–EUROCRYPT’92 (1993), R. A. Rueppel, Ed., vol. 658 of Lecture Notes in Computer Science, pp. 200–207.
4. Clavier, C., and Joye, M. Universalexp onentiation algorithm–a first step towards provable SPA-resistance. In Cryptographic Hardware and Embedded Systems–CHES 2001 (2001), Ç. K. Koç, D. Naccache, and C. Paar, Eds., vol. 2162 of Lecture Notes in Computer Science, pp. 300–308.
5. Coron, J.-S. Resistance against differential power analysis for elliptic curve cryptosystems. In Cryptographic Hardware and Embedded Systems–CHES’99 (1999), Ç. K. Koç and C. Paar, Eds., vol. 1717 of Lecture Notes in Computer Science, pp. 292–302.
6. Fischer, W., Giraud, C., Knudsen, E. W., and Jean-Pierre, S. Parallel scalar multiplication on general elliptic curves over Fp hedged against nondifferentialside-c hannelattac ks. Cryptology ePrint Archive Report 2002/007, 2002. Available from http://eprint.iacr.org/.
7. Institute of Electrical and Electronics Engineers (IEEE). IEEE stand ard specifications for public-key cryptography. IEEE Std 1363-2000, 2000.
8. Itoh, K., Takenaka, M., Torii, N., Temma, S., and Kurihara, Y. Fast implementation of public-key cryptography on a DSP TMS320C6201. In Cryptographic Hardware and Embedded Systems–CHES’99 (1999), Ç. K. Koç and C. Paar, Eds., vol. 1717 of Lecture Notes in Computer Science, pp. 61–72.
9. Izu, T., and Takagi, T. A fast parallel elliptic curve multiplication resistant against side channelattacks. In Public Key Cryptography–PKC 2002 (2002), D. Naccache and P. Paillier, Eds., vol. 2274 of Lecture Notes in Computer Science, pp. 280–296.
10. Knuth, D. E. The Art of Computer Programming–Vol. 2: Seminumerical Algorithms (2nde d.). Addison-Wesley, 1981.
11. Knuth, D. E. The Art of Computer Programming–Vol. 2: Seminumerical Algorithms (3rde d.). Addison-Wesley, 1998.
12. Kocher, P. C. Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In Advances in Cryptology–CRYPTO’96 (1996), N. Koblitz, Ed., vol. 1109 of Lecture Notes in Computer Science, pp. 104–113.
13. Kocher, P. C., Jaffe, J., and Jun, B. Differentialp ower analysis. In Advances in Cryptology–CRYPTO’99 (1999), M. Wiener, Ed., vol. 1666 of Lecture Notes in Computer Science, pp. 388–397.
14. Messerges, T. S. Using second-order power analysis to attack DPA resistant software. In Cryptographic Hardware and Embedded Systems–CHES 2000 (2000), Ç. K. Koç and C. Paar, Eds., vol. 1965 of Lecture Notes in Computer Science, pp. 238–251.
15. Möller, B. Securing elliptic curve point multiplication against side-channel attacks. In Information Security–ISC 2001 (2001), G. I. Davida and Y. Frankel, Eds., vol. 2200 of Lecture Notes in Computer Science, pp. 324–334.
16. Möller, B. Securing elliptic curve point multiplication against side-channel attacks, addendum: Efficiency improvement. http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller/ecc-scaisc01.pdf, 2001.
17. Montgomery, P. L. Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation 48 (1987), 243–264.
18. Okeya, K. Method of calculating multiplication by scalars on an elliptic curve and apparatus using same. European Patent EP1160661, 2001.
19. Okeya, K., and Sakurai, K. Power analysis breaks elliptic curve cryptosystems even secure against the timing attack. In Progress in Cryptology–INDOCRYPT 2000 (2000), B. K. Roy and E. Okamoto, Eds., vol. 1977 of Lecture Notes in Computer Science, pp. 178–190.
20. Okeya, K., and Sakurai, K. A second-order DPA attack breaks a windowmethod based countermeasure against side channelattacks. In Information Security–ISC 2002 (these proceedings), A. H. Chan and V. Gligor, Eds.
21. Schindler, W. A combined timing and power attack. In Public Key Cryptography–PKC 2002 (2002), D. Naccache and P. Paillier, Eds., vol. 2274 of Lecture Notes in Computer Science, pp. 263–279.
22. Vadekar, A., and Lambert, R. J. Timing attack resistant cryptographic system. Patent Cooperation Treaty (PCT) Publication WO 00/05837, 2000.
23. Vanstone, S. A., and Gallant, R. P. Power signature attack resistant cryptography. Patent Cooperation Treaty (PCT) Publication WO 00/25204, 2000.
24. Walter, C. D., and Thompson, S. Distinguishing exponent digits by observing modular subtractions. In Progress in Cryptology–CT-RSA 2001 (2001), D. Naccache, Ed., vol. 2020 of Lecture Notes in Computer Science, pp. 192–207.
25. Yao, A. C. -C. On the evaluation of powers. SIAM Journal on Computing 5 (1976), 100–103.