Twisted edwards curves revisited

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

Volumn 5350 LNCS, Issue , 2008, Pages 326-343

  Hisil, Huseyin ^a   Wong, Kenneth Koon Ho ^a   Carter, Gary ^a   Dawson, Ed ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Efficient elliptic curve arithmetic; Side channel attack; SPA; Unified addition

Indexed keywords

APPLICATIONS; DIGITAL ARITHMETIC; STATISTICAL PROCESS CONTROL;

ADDITION ALGORITHMS; EFFICIENT ELLIPTIC CURVE ARITHMETIC; ELLIPTIC CURVE CRYPTOGRAPHIES; ELLIPTIC CURVES; FAST ALGORITHMS; FASTER IMPLEMENTATIONS; GROUP OPERATIONS; POINT ADDITIONS; SCALAR MULTIPLICATIONS; SIDE CHANNEL ATTACK; SIMPLE POWER ANALYSIS; SPA; SPEED INCREASES; SPEED LIMITS; UNIFIED ADDITION;

CRYPTOGRAPHY;

EID: 58349103020     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-89255-7_20     Document Type: Conference Paper

References (24)

1. Bernstein, D.J., Birkner, P., Joye. M., Lange. T., Peters, C.: Twisted Edwards curves. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 389-405. Springer, Heidelberg (2008)
2. Bernstein, D.J., Birkner, P., Lange, T., Peters, C.: Optimizing double-base ellipticcurve single-scalar multiplication. In: Srinathan, K., Rangan, C.P., Yung, M. (eds.) INDOCRYPT 2007. LNCS, vol. 4859, pp. 167-182. Springer, Heidelberg (2007)
3. Bernstein, D.J., Birkner, P., Lange, T., Peters, C.: ECM using Edwards curves. Cryptology ePrint Archive, Report 2008/016 (2008), http://eprint.iacr. org/
4. Bernstein, D.J., Lange, T.: Explicit-formulas database (2007), http://www.hyperelliptic.org/EFD
5. Bernstein, D.J., Lange, T.: Faster addition and doubling on elliptic curves. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 29-50. Springer, Heidelberg (2007)
6. Bernstein, D.J., Lange, T.: Inverted Edwards coordinates. In: Boztaş, S., Lu, H.-F. (eds.) AAECC 2007. LNCS, vol. 4851, pp. 20-27. Springer, Heidelberg (2007)
7. Billet, O., Joye, M.: The Jacobi model of an elliptic curve and side-channel analysis. In: Fossorier, M.P.C. Hoholdt, T., Poli, A. (eds.) AAECC 2003. LNCS. vol. 2643, pp. 34-42. Springer, Heidelberg (2003)
8. Brier, E., Joye, M.: Weierstraß elliptic curves and side-channel attacks. In: Naccache. D., Paillier, P. (eds.) PKC 2002. LNCS. vol. 2274, pp. 335-345. Springer, Heidelberg (2002)
9. Brier. E., Joye. M.: Fast point multiplication on elliptic curves through isogenies. In: Fossorier, M.P.C. Hoholdt, T., Poli, A. (eds.) AAECC 2003. LNCS. vol. 2643, pp. 43-50. Springer, Heidelberg (2003)
10. Cohen. H., Frey, G. (eds.): Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC Press. Boca Raton (2005)
11. Cohen. H., Miyaji, A., Ono. T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 51-65. Springer, Heidelberg (1998)
12. Doche. C. Icart, T., Kohel, D.R.: Efficient scalar multiplication by isogeny decompositions. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 191-206. Springer, Heidelberg (2006)
13. Edwards, H.M.: A normal form for elliptic curves. Bulletin of the AMS 44(3). 393-422 (2007)
14. Eisenträger, K., Lauter, K., Montgomery, P.L.: Fast elliptic curve arithmetic and improved Weil pairing evaluation. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 343-354. Springer, Heidelberg (2003)
15. p, hedged against non-differential side-channel attacks. Cryptology ePrint Archive, Report 2002/007 (2002), http://eprint.iacr.org/
16. Gaudry, P., Lubicz, D.: The arithmetic of characteristic 2 Kummer surfaces. Cryptology ePrint Archive, Report 2008/133 (2008), http://eprint.iacr.org/
17. Hisil, H., Wong, K., Carter, G., Dawson, E.: Faster group operations on elliptic curves. Cryptology ePrint Archive, Report 2007/441 (2007), http://eprint.iacr.org/
18. Izu, T., Takagi, T.: A fast parallel elliptic curve multiplication resistant against side channel attacks. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 280-296. Springer, Heidelberg (2002)
19. Izu, T., Takagi, T.: Exceptional procedure attack on elliptic curve cryptosystems. In: Desmedt. Y.G. (ed.) PKC 2003. LNCS, vol. 2567. pp. 224-239. Springer, Heidelberg (2003)
20. Joye, M., Quisquater, J.J.: Hessian elliptic curves and side-channel attacks. In: Koç, Ç.K., Naccache, D., Paar. C (eds.) CHES 2001. LNCS, vol. 2162. pp. 402-410. Springer, Heidelberg (2001)
21. Joye. M., Yen. S.M.: The Montgomery powering ladder. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS. vol. 2523, pp. 291-302. Springer. Heidelberg (2003)
22. Liardet, P.Y., Smart. N.P.: Preventing SPA/DPA in ECC systems using the Jacobi form. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS. vol. 2162, pp. 391-401. Springer, Heidelberg (2001)
23. Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation 48(177), 243-264 (1987)
24. de Rooij, P.: Efficient exponentiation using precomputation and vector addition chains. In: De Santis. A. (ed.) EUROCRYPT 1994. LNCS, vol. 950. pp. 389-399. Springer, Heidelberg (1995)