1. 17th annual symposium on foundations of computer science. IEEE Computer Society, Long Beach (1976); MR 56:1766. See [52].

   Google Scholar 

2. Alster, K., Urbanowicz, J., Williams, H.C. (eds.): Public-key cryptography and computational number theory: proceedings of the international conference held in Warsaw, September 11–15, 2000. Walter de Gruyter, Berlin (2001); ISBN 3–11–017046–9. MR 2002h:94001. See [60]

   MATH  Google Scholar 

3. Antipa, A., Brown, D., Menezes, A., Struik, R., Vanstone, S.: Validation of elliptic curve public keys. In: [21], pp. 211–223 (2003); MR 2171928. Citations in this paper: §1

   Google Scholar 

4. Avanzi, R.M.: Aspects of hyperelliptic curves over large prime fields in software implementations. In: [36], pp. 148–162 (2004); Citations in this paper: §1, §5

   Google Scholar 

5. Avanzi, R.M.: Generic algorithms for computing discrete logarithms. In: [19], pp. 477–494 (2005); MR 2162735. Citations in this paper: §3, §3

   Google Scholar 

6. Avanzi, R.M., Mihăilescu, P.: Generic efficient arithmetic algorithms for PAFFs (processor adequate finite fields) and related algebraic structures (extended abstract). In: [43], pp. 320–334 (2004); Citations in this paper: §4

   Google Scholar 

7. Bailey, D.V., Paar, C.: Efficient arithmetic in finite field extensions with application in elliptic curve cryptography. Journal of Cryptology 14, 153–176 (2001); ISSN 0933–2790. Citations in this paper: §1, §4

   Article MathSciNet MATH  Google Scholar 

8. Bellare, M. (ed.): CRYPTO 2000. LNCS, vol. 1880. Springer, Heidelberg (2000); ISBN 3–540–67907–3. MR 2002c:94002. See [14]

   MATH  Google Scholar 

9. Bender, A., Castagnoli, G.: On the implementation of elliptic curve cryptosystems. In: [16], pp. 186–192 (1990); MR 91d:11154. Citations in this paper: §4

   Google Scholar 

10. Bentahar, K.: The equivalence between the DHP and DLP for elliptic curves used in practical applications (revisited, 2005); Citations in this paper: §3,http://eprint.iacr.org/2005/307

11. Bernstein, D.J.: The Poly1305-AES message-authentication code. In: [32], pp. 32–49 (2005); ID 0018d9551b5 546d97c340e0dd8cb5750. Citations in this paper: §4,http://cr.yp.to/papers.html#poly1305

12. Bernstein, D.J.: Cache-timing attacks on AES (2005); ID cd9faae9bd5308c440df50fc26a517b4. Citations in this paper: §1, §4,http://cr.yp.to/papers.html#cachetiming

13. Bernstein, D.J.: Salsa20 specification (2005); Citations in this paper: §3,http://cr.yp.to/snuffle.html

14. Biehl, I., Meyer, B., Müller, V.: Differential fault attacks on elliptic curve cryptosystems (extended abstract). In: [8], pp. 131–146 (2000); Citations in this paper: §1, §3,http://lecturer.ukdw.ac.id/vmueller/publications.php

15. Boyd, C. (ed.): ASIACRYPT 2001. LNCS, vol. 2248. Springer, Heidelberg (2001); ISBN 3–540–42987–5. MR 2003d:94001. See [59]

    MATH  Google Scholar 

16. Brassard, G. (ed.): CRYPTO 1989. LNCS, vol. 435. Springer, Heidelberg (1990); ISBN 0–387–97317–6. MR 91b:94002. See [9]

    MATH  Google Scholar 

17. Brown, M., Hankerson, D., López, J., Menezes, A.: Software implementation of the NIST elliptic curves over prime fields (2000); see also newer version [18]. Citations in this paper: §1, §5,http://www.cacr.math.uwaterloo.ca/techreports/2000/corr2000-56.ps

18. Brown, M., Hankerson, D., López, J., Menezes, A.: Software implementation of the NIST elliptic curves over prime fields. In: [49], pp. 250–265 (2001); see also older version [17]. MR 1907102

    Google Scholar 

19. Cohen, H., Frey, G. (eds.): Handbook of elliptic and hyperelliptic curve cryptography. CRC Press, Boca Raton (2005); ISBN 1–58488–518–1. See [5], [24], [25], [30]

    Google Scholar 

20. Desmedt, Y. (ed.): CRYPTO 1994. LNCS, vol. 839. Springer, Heidelberg (1994); See [44]

    MATH  Google Scholar 

21. Desmedt, Y. (ed.): PKC 2003. LNCS, vol. 2567. Springer, Heidelberg (2002); ISBN 3–540–00324–X. See [3]

    MATH  Google Scholar 

22. Diem, C.: The GHS attack in odd characteristic. Journal of the Ramanujan Mathematical Society 18, 1–32 (2003); MR 2004a:14030. Citations in this paper: §4,http://www.math.uni-leipzig.de/~diem/preprints

    MathSciNet MATH  Google Scholar 

23. Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory 22, 644–654 (1976); ISSN 0018–9448. MR 55:10141. Citations in this paper: §3,http://cr.yp.to/bib/entries.html#1976/diffie

    Article MathSciNet MATH  Google Scholar 

24. Doche, C., Lange, T.: Arithmetic of elliptic curves. In: [19], pp. 267–302 (2005); MR 2162729. Citations in this paper: §A

    Google Scholar 

25. Doche, C., Lange, T.: Arithmetic of special curves. In: [19], pp. 355–387 (2005); MR 2162731. Citations in this paper: §4

    Google Scholar 

26. Fong, K., Hankerson, D., López, J., Menezes, A.: Field inversion and point halving revisited (2003); see also newer version [27]. Citations in this paper: §1,http://www.cacr.math.uwaterloo.ca/techreports/2003/techreports2003.html

27. Fong, K., Hankerson, D., López, J., Menezes, A.: Field inversion and point halving revisited. IEEE Transactions on Computers 53, 1047–1059 (2004); see also older version [26]. ISSN 0018–9340

    Article  Google Scholar 

28. Franke, J., Kleinjung, T., Paar, C., Pelzl, J., Priplata, C., Simka, M., Stahlke, C.: In: Workshop Record of SHARCS 2005, pp. 51–62 (2005); Citations in this paper: §3, §3,http://www.best.tuke.sk/simka/pub.html

29. Frey, G.: How to disguise an elliptic curve, Weil descent (1998); Citations in this paper: §4,http://www.cacr.math.uwaterloo.ca/conferences/1998/ecc98/slides.html

30. Frey, G., Lange, T.: Transfer of discrete logarithms. In: [19], pp. 529–543 (2005); MR 2162738. Citations in this paper: §3

    Google Scholar 

31. Robert, P., Gallant, R.J., Lambert, S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In: [38], pp. 190–200 (2001); MR 2003h:14043. Citations in this paper: §5.

    Google Scholar 

32. Gilbert, H., Handschuh, H. (eds.): FSE 2005. LNCS, vol. 3557. Springer, Heidelberg (2005); ISBN 3–540– 26541–4. See [11].

    Google Scholar 

33. Hankerson, D., Hernandez, J.L., Menezes, A.: Software implementation of elliptic curve cryptography over binary fields (2000); Citations in this paper: §1, see also newer version [34],http://www.cacr.math.uwaterloo.ca/techreports/2000/corr2000-42.ps

34. Hankerson, D., Hernandez, J.L., Menezes, A.: Software implementation of elliptic curve cryptography over binary fields. In: [40], pp. 1–24 (2000); see also older version [33]

    Google Scholar 

35. Hankerson, D., Menezes, A., Vanstone, S.: Guide to elliptic curve cryptography. Springer, New York (2004); ISBN 0–387–95273–X. MR 2054891. Citations in this paper: §4

    MATH  Google Scholar 

36. Joye, M., Quisquater, J.-J. (eds.): CHES 2004. LNCS, vol. 3156. Springer, Heidelberg (2004); ISBN 3–540–22666–4. See [4]

    MATH  Google Scholar 

37. Kaliski Jr., B.S. (ed.): CRYPTO 1997. LNCS, vol. 1294. Springer, Heidelberg (1997); ISBN 3–540–63384–7. MR 99a:94041. See [42]

    MATH  Google Scholar 

38. Kilian, J. (ed.): CRYPTO 2001. LNCS, vol. 2139. Springer, Heidelberg (2001); ISBN 3–540–42456–3. MR 2003d:94002. See [31]

    MATH  Google Scholar 

39. Koblitz, N., Menezes, A.J.: Another look at provable security (2004); Citations in this paper: §3,http://www.cacr.math.uwaterloo.ca/~ajmeneze/publications/provable.pdf

40. Ko̧c, Ç.K., Paar, C.: CHES 2000. LNCS, vol. 1965. Springer, Heidelberg (2000); ISBN 3–540–42521–7. See [34]

    Book  Google Scholar 

41. Kuhn, F., Struik, R.: Random walks revisited: extensions of Pollard’s rho algorithm for computing multiple discrete logarithms. In: [64], pp. 212–229 (2001); Citations in this paper: §3,http://www.distcomp.ethz.ch/publications.html

42. Lim, C.H., Lee, P.J.: A key recovery attack on discrete log-based schemes using a prime order subgroup. In: [37], pp. 249–263 (1997); Citations in this paper: §3, §3,http://dasan.sejong.ac.kr/~chlim/english_pub.html

43. Matsui, M., Zuccherato, R.: SAC 2003. LNCS, vol. 3006. Springer, Heidelberg (2004); ISBN 3–540–21370–8. See [6]

    Book MATH  Google Scholar 

44. Maurer, U.M.: Towards the equivalence of breaking the Diffie-Hellman protocol and computing discrete logarithms. In: [20], pp. 271–281 (1994); Citations in this paper: §3,http://www.crypto.ethz.ch/~maurer/publications.html

45. Menezes, A.: Another look at HMQV (2005); Citations in this paper: §2,http://eprint.iacr.org/2005/205

46. Miller, V.S.: Use of elliptic curves in cryptography. In: [65], pp. 417–426 (1986); MR 88b:68040. Citations in this paper: §1

    Google Scholar 

47. Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation 48, 243–264 (1987); ISSN 0025–5718. Citations in this paper: §5,http://cr.yp.to/bib/entries.html#1987/montgomery

    Article MathSciNet MATH  Google Scholar 

48. Muzereau, A., Smart, N.P., Vercauteren, F.: The equivalence between the DHP and DLP for elliptic curves used in practical applications. LMS Journal of Computation and Mathematics 7, 50–72 (2004); Citations in this paper: §3,http://www.lms.ac.uk/jcm/7/lms2003-034/

    Article MathSciNet MATH  Google Scholar 

49. Naccache, D. (ed.): CT-RSA 2001. LNCS, vol. 2020. Springer, Heidelberg (2001); ISBN 3– 540–41898–9. MR 2003a:94039. See [18]

    MATH  Google Scholar 

50. Osvik, D.A., Shamir, A., Tromer, E.: Cache atacks and countermeasures: the case of AES, extended version (2005); Citations in this paper: §1,http://www.wisdom.weizmann.ac.il/~tromer/

51. Percival, C.: Cache missing for fun and profit (2005); Citations in this paper: §1,http://www.daemonology.net/hyperthreading-considered-harmful/

52. Pippenger, N.: On the evaluation of powers and related problems (preliminary version). In: [1], pp. 258–263 (1976); newer version split into [53] and [54]. MR 58:3682. Citations in this paper: §5,http://cr.yp.to/bib/entries.html#1976/pippenger

53. Pippenger, N.: The minimum number of edges in graphs with prescribed paths. Mathematical Systems Theory 12, 325–346 (1979); see also older version [52], ISSN 0025–5661. MR 81 e:05079,http://cr.yp.to/bib/entries.html#1979/pippenger

    Article MathSciNet MATH  Google Scholar 

54. Pippenger, N.: On the evaluation of powers and monomials. SIAM Journal on Computing 9, 230–250 (1980); see also older version [52]. ISSN 0097–5397. MR 82c:10064,http://cr.yp.to/bib/entries.html#1980/pippenger

    Article MathSciNet MATH  Google Scholar 

55. Pollard, J.M.: Kangaroos, Monopoly and discrete logarithms. Journal of Cryptology 13, 437–447 (2000); ISSN 0933–2790. Citations in this paper: §3

    Article MathSciNet MATH  Google Scholar 

56. Proos, J., Zalka, C.: Shor’s discrete logarithm quantum algorithm for elliptic curves (2003); Citations in this paper: §1,http://www.cacr.math.uwaterloo.ca/techreports/2003/tech_reports2003.html

57. Smart, N.P.: A comparison of different finite fields for use in elliptic curve cryptosystems (2000); see also newer version [58],http://www.cs.bris.ac.uk/Publications/pub_info.jsp?id=1000458

58. Smart, N.P.: A comparison of different finite fields for elliptic curve cryptosystems. Computers and Mathematics with Applications 42, 91–100 (2001); see also older version [57]. MR 2002c:94033. Citations in this paper: §1

    Article MathSciNet MATH  Google Scholar 

59. Stam, M., Lenstra, A.K.: Speeding up XTR. In: [15], pp. 125–143 (2001); MR 2003h:94049. Citations in this paper: §5

    Google Scholar 

60. Teske, E.: Square-root algorithms for the discrete logarithm problem (a survey). In: [2], pp. 283–301 (2001); MR 2003c:11156. Citations in this paper: §3,http://www.cacr.math.uwaterloo.ca/~eteske/publications.html

61. Teske, E.: Computing discrete logarithms with the parallelized kangaroo method (2001); see also newer version [62]. Citations in this paper: §3,http://www.cacr.math.uwaterloo.ca/techreports/2001/tech_reports2001.html

62. Teske, E.: Computing discrete logarithms with the parallelized kangaroo method. Discrete Applied Mathematics 130, 61–82 (2003); see also older version [61]. MR 2004h:11112

    Article MathSciNet MATH  Google Scholar 

63. van Oorschot, P.C., Wiener, M.: Parallel collision search with cryptanalytic applications. Journal of Cryptology 12, 1–28 (1999); ISSN 0933–2790. Citations in this paper: §3,http://members.rogers.com/paulv/papers/pubs.html

    Article MathSciNet MATH  Google Scholar 

64. Vaudenay, S., Youssef, A.M. (eds.): SAC 2001. LNCS, vol. 2259. Springer, Heidelberg (2001); ISBN 3–540–43066–0. MR 2004k:94066. See [41]

    MATH  Google Scholar 

65. Williams, H.C. (ed.): CRYPTO 1985. LNCS, vol. 218. Springer, Heidelberg (1986); ISBN 3–540–16463–4. See [46]

    Google Scholar 

Download references