A fast parallel implementation of elliptic curve point multiplication over GF(2m)

Microprocessors and Microsystems

Volumn 28, Issue 5-6 SPEC. ISS., 2004, Pages 329-339

  Rodríguez Henríquez, Francisco ^a   Saqib, Nazar Abbas ^a   Díaz Pérez, Arturo ^a  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

Elliptic curve cryptography; Finite field arithmetic; Karatsuba Ofman multipliers

Indexed keywords

COMPUTATIONAL METHODS; CRYPTOGRAPHY; FIELD PROGRAMMABLE GATE ARRAYS; PROBLEM SOLVING; SET THEORY;

ELLIPTIC CURVE CRYPTOGRAPHY; FINITE FIELD ARITHMETIC; KARATSUBA-OFMAN MULTIPLIERS; PARALLEL IMPLEMENTATION;

MICROPROCESSOR CHIPS;

EID: 2642579951     PISSN: 01419331     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.micpro.2004.03.003     Document Type: Article

References (27)

1. Koblitz N. Elliptic curve cryptosystems. Mathematics of Computation. 48:(177):1987;203-209.
2. Miller V. Uses of elliptic curves in cryptography. Williams H.C. Advances in Cryptology-CRYPTO 85 Proceedings. Lecture Notes in Computer Science. vol. 218:1985;417-426.
3. Chudnovsky D.V., Chudnovsky G.V. Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Advances in Applied Mathematics. 7:1986;385-434.
4. Satoh A., Takano K. A scalable dual-field elliptic curve cryptographic processor. IEEE Transactions on Computers. 52:(4):2003;449-460.
5. Schroeppel R., Beaver C., Gonzales R., Miller R., Draelos T. A low-power design for an elliptic curve digital signature chip. Cryptographic Hardware and Embedded Systems-CHES 2002, fourth International Workshop, Redwood Shores, CA, USA, August 13-15, 2002, Revised Papers. 2523:2003;366-380.
6. Orlando G., Paar C. A high-performance reconfigurable elliptic curve processor for GF(2m), Cryptographic Hardware and Embedded Systems-CHES. Second International Workshop, Worcester, MA, USA, August 17-18, 2000, Proceedings. 1965:2000;41-56.
7. Smart N. The Hessian form of an elliptic curve. Cryptographic Hardware and Embedded Systems-CHES, Third International Workshop, Paris, France, May 14-16, 2001, Proceedings. 2162:2001;118-125.
8. Gura N., Shantz S., An H.E., , et al. end-to-end systems approach to elliptic curve cryptography. Cryptographic Hardware and Embedded Systems-CHES 2002, 4th International Workshop, Redwood Shores, CA, USA, August 13-15, 2002, Revised Papers. 2523:2003;349-365.
9. Ernst M., Jung M., Madlener F., , et al. A reconfigurable system on chip implementation for elliptic curve cryptography over GF(2n), Cryptographic Hardware and Embedded Systems-CHES 2002. 4th International Workshop, Redwood Shores, CA, USA, August 13-15, 2002, Revised Papers. 2523:2003;381-399.
10. Bednara M., Daldrup M., Shokrollahi J., Teich J., von zur Gathen J. Reconfigurable implementation of elliptic curve crypto algorithms. Proceedings of the Ninth Reconfigurable Architectures Workshop (RAW-02), Fort Lauderdale, Florida, USA. 2002.
11. McEliece R.J. Finite fields for computer scientists and engineers. 1987;Kluwer, Boston, MA.
12. Menezes A.J., Blake I.F., Gao X., Mullen R.C., Vanstone S.A., Yaghoobian T. Applications of Finite Fields. 1993;Kluwer, Boston, MA.
13. Wicker S.B., Bhargava V.K. Reed-Solomon Codes and Their Applications. 1994;Prentice-Hall, Englewood Cliffs, NJ.
14. Hasan M.A., Wang M.Z., Bhargava V.K. A modified Massey-Omura parallel multiplier for a class of finite fields. IEEE Transactions on Computers. 42:(10):1993;1278-1280.
15. Sunar B., Koç Ç.K. Mastrovito multiplier for all trinomials. IEEE Transactions on Computers. 48:(5):1999;522-527.
16. Morii M., Kasahara M., Whiting D.L. Efficient bit-serial multiplication and the discrete-time Wiener-Hopf equation over finite fields. IEEE Transactions on Information Theory. 35:(6):1989;1177-1183.
17. Wu H., Hasan M.A. Low complexity bit-parallel multipliers for a class of finite fields. IEEE Transactions on Computers. 47:(8):1998;883-887.
18. Zhang T., Parhi K. Systematic design of original and modified mastrovito multipliers for general irreducible polynomials. IEEE Transactions on Computers. 50:(7):2001;734-749.
19. Halbutogullari A., Koç Ç.K. Mastrovito multiplier for general irreducible polynomials. IEEE Transactions on Computers. 49:(5):2000;503-518.
20. Paar C. A new architecture for a parallel finite field multiplier with low complexity based on composite fields. IEEE Transactions on Computers. 45:(7):1996;856-861.
21. Bach E., Shallit J. Algorithmic number theory, Volume I: efficient algorithms. 1996;Kluwer, Boston, MA.
22. Guajardo J., Paar C. Efficient algorithms for elliptic curve cryptosystems. Kaliski B.S. Jr. Advances in Cryptology - CRYPTO 97 Lecture Notes in Computer Science. 1294:1997;342-356.
23. I. P1363, Standard specifications for public-key cryptography, draft version 7 Edition, IEEE standards documents, 1998, http://grouper.ieee.org/ groups/1363/.
24. Grabbe C., Bednara M., , et al. FPGA designs of parallel high performance gf(2233) multipliers. IEEE International Symposium on Circuits and Systems (ISCAS-03), Bangkok, Thailand. 2003;. pp. 268-271.
25. m) . in: International Conference on Computer Science and Technology (CST 2003), Cancun, Mexico. 2003.
26. m ) without precomputation. Cryptographic Hardware and Embedded Systems, First International Workshop, CHES'99, Worcester, MA, USA, August 12-13, Proceedings. 1717:(1999):1999;316-327.
27. Hankerson D., Lopez-Hernandez J., Menezes A. Software implementation of elliptic curve cryptography over binary fields. Cryptographic Hardware and Embedded Systems-CHES, Second International Workshop, Worcester, MA, USA, August 17-18, 2000, Proceedings. 1965:2000;1-24.