Software implementation of the nist elliptic curves over prime fields

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

Volumn 2020, Issue , 2001, Pages 250-265

  Brown, Michael ^a   Hankerson, Darrel ^b,d   López, Julio ^c   Menezes, Alfred ^a,d  

^a UNIVERSITY OF WATERLOO   (Canada)

^b AUBURN UNIVERSITY   (United States)

^c UNIVERSIDAD DEL VALLE   (Colombia)

^d Certicom Research   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY;

BINARY FIELDS; ELLIPTIC CURVE; PENTIUM; PRIME FIELD; SOFTWARE IMPLEMENTATION;

CRYPTOGRAPHY;

EID: 84937564555     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45353-9_19     Document Type: Conference Paper

References (23)

1. ANSI X9. 62, Public Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA), 1999.
2. A. Bosselaers, R. Govaerts and J. Vandewalle, “Comparison of three modular re-duction functions", Crypto '93, LNCS 773, 1994, 175-186.
3. E. Brickell, D. Gordon, K. McCurley and D. Wilson, “Fast exponentiation with preecomputation", Eurocrypt '92, LNCS 658, 1993, 200-207.
4. D. Chudnovsky and G. Chudnovsky, “Sequences of numbers generated by addition in formal groups and new primality and factoring tests", Advances in Applied Mathematics, 7 (1987), 385-434.
5. H. Cohen, A. Miyaji and T. Ono, “Efficient elliptic curve exponentiation using mixed coordinates", Asiacrypt '98, LNCS 1514, 1998, 51-65.
6. E. De Win, S. Mister, B. Preneel and M. Wiener, “On the performance of signature schemes based on elliptic curves", Proc. ANTS-III, LNCS 1423, 1998, 252-266.
7. J. Guajardo and C. Paar, “Modified squaring algorithm", preprint, 1999.
8. D. Hankerson, J. Hernandez and A. Menezes, “Software implementation of elliptic curve cryptography over binary ffelds", Proc. CHES 2000, to appear.
9. T. Hasegawa, J. Nakajima and M. Matsui, “A practical implementation of ellip-tic curve cryptosystems over GF(p) on a 16-bit microcomputer", Proc. PKC '98, LNCS 1431, 1998, 182-194.
10. IEEE 1363-2000, Standard Specifications for Public-Key Cryptography, 2000.
11. ISO/IEC 15946, Information Technology-Security Techniques-Cryptographic Techniques Based on Elliptic Curves, Committee Draft (CD), 1999.
12. K. Itoh et al. “Fast implementation of public-key cryptography on a DSP TMS320C6201", Proc. CHES '99, LNCS 1717, 1999, 61-72.
13. D. Knuth, The Art of Computer Programming-Seminumerical Algorithms, Addison-Wesley, 3rd edition, 1998.
14. N. Koblitz, “Elliptic curve cryptosystems", Math. Comp., 48 (1987), 203-209.
15. C. Lim and P. Lee, “More flexible exponentiation with precomputation", Crypto '94, LNCS 839, 1994, 95-107.
16. A. Menezes, P. van Oorschot and S. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997.
17. V. Miller, “Uses of elliptic curves in cryptography", Crypto '85, LNCS 218, 1986, 417-426.
18. A. Miyaji, T. Ono and H. Cohen, “Efficient elliptic curve exponentiation", Procee-dings of ICICS '97, LNCS 1334, 1997, 282-290.
19. F. Morain and J. Olivos, “Speeding up the computations on an elliptic curve using addition-subtraction chains", Inform. Th. Appl. 24 (1990), 531-544.
20. NIST, Digital Signature Standard, FIPS Publication 186-2, February 2000.
21. NIST, Advanced Encryption Standard, work in progress.
22. J. Solinas, “Generalized Mersenne numbers", Technical Report CORR 99-39, Dept. of C&O, University of Waterloo, 1999.
23. J. Solinas, “Efficient arithmetic on Koblitz curves", Designs, Codes and Crypto-graphy, 19 (2000), 195-249.