Overlap-free Karatsuba-Ofman polynomial multiplication algorithms

IET Information Security

Volumn 4, Issue 1, 2010, Pages 8-14

  Fan, H ^a   Sun, J ^a   Gu, M ^a   Lam, K Y ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

KARATSUBA-OFMAN ALGORITHM; POLYNOMIAL MULTIPLICATION; VLSI IMPLEMENTATION; XOR GATES;

EID: 75949124148     PISSN: 17518709     EISSN: 17518717     Source Type: Journal    
DOI: 10.1049/iet-ifs.2009.0039     Document Type: Article

References (34)

1. Karatsuba, A., and Ofman, Y.: ' Multiplication of multidigit numbers on automata ', Sov. Phys.-Dokl. (English translation), 1963, 7, (7), p. 595-596
2. Afanasyev, V.B.: ' Complexity of VLSI implementation of finite field arithmetic ', Proc. II. Intern. Workshop on Algebraic and Combinatorial Coding Theory, 1990, p. 6-7
3. Paar, C.: ' Efficient VLSI architectures for bit-parallel computation in Galois fields ', 1994, PhD, University of Essen, Germany
4. Paar, C.: ' A new architecture for a parallel finite field multiplier with low complexity based on composite fields ', IEEE Trans. Comput., 1996, 45, (7), p. 856-861 0018-9340
5. 4n) ', IEEE Trans. Comput., 1998, 47, (2), p. 162-170 0018-9340
6. k+1 ', IEE Electron. Lett., 1999, 35, (7), p. 551-552
7. Leone, M.: ' A new low complexity parallel multiplier for a class of finite fields ', Proc. Cryptographic Hardware and Embedded Systems (CHES 2001), 2001, p. 160-170, (LNCS, 2162)
8. n) ', Proc. IEEE Workshop Heterogeneous reconfigurable Systems on Chip, 2002
9. n) ', Proc. Cryptographic Hardware and Embedded Systems (CHES 2002), 2003, p. 381-399, (LNCS, 2523)
10. 233) multipliers ', Proc. Int. Symp. on Circuits and Systems (ISCAS 2003), 2003, II, p. 268-271
11. Weimerskirch, A., and Paar, C.: ' Generalizations of the Karatsuba algorithm for efficient implementations ', 2003), Available at: http://www.crypto.ruhr-uni-bochum.de/imperia/md/content/texte/kaweb.pdf
12. m) ', Proc. Int. Conf. Computer Science and Technology (CST 2003), 2003, p. 405-410
13. Erdem, S.S., and Koç, C.K.: ' A less recursive variant of Karatsuba-Ofman algorithm for multiplying operands of size a power of two ', Proc. 16th IEEE Symp. on Computer Arithmetic (Arith-16 2003), 2003, p. 28-35
14. k) multipliers ', IEEE Trans. Comput., 2004, 53, (9), p. 1097-1105 0018-9340
15. Chang, N.S., Kim, C.H., Park, Y.H., and Lim, J.: ' A non-redundant and efficient architecture for Karatsuba-Ofman algorithm ', Proc. Eighth Int. Conf. on Information Security (ISC 2005), 2005, p. 288-299, (LNCS, 3650)
16. Montgomery, P.L.: ' Five, six, and seven-term Karatsuba-like formulae ', IEEE Trans. Comput., 2005, 54, (3), p. 362-369 0018-9340
17. Fan, H., and Hasan, M.A.: ' Comments on "five, six, and seven-term Karatsuba-like formulae" ', IEEE Trans. Comput., 2007, 56, (5), p. 716-717 0018-9340
18. Dyka, Z., and Langendoerfer, P.: ' Area efficient hardware implementation of elliptic curve cryptography by iteratively applying Karatsuba's method ', Proc. Conf. on Design, Automation and Test in Europe 2005, 2005, p. 70-75 (Pubitemid 44172207)
19. m) defined by all-one polynomials using redundant representation ', IEEE Trans. Comput., 2005, 54, (12), p. 1628-1630 0018-9340
20. n) ', Proc. 23rd Biennial Symp. on Communications, 2006
21. 2 ', Proc. 12th Workshop on Selected Areas in Cryptography (SAC 2005), 2006, p. 359-369, (LNCS, 3897)
22. 2 in hardware ', Proc. IEEE Workshop on Information Theory, 2006, p. 107-111
23. m) and its application to ECC designs ', Proc. Conf. on Design, Automation and Test in Europe 2007, 2007, p. 1253-1258
24. Gathen, J.V.Z., and Gerhard, J.: ' Modern computer algebra ', (Cambridge University Press, 1999), 1st edn., 2nd edn., 2003
25. Moenck, R.T.: ' Practical fast polynomial multiplication ', Proc. 1976 ACM. Symp. on Symbolic and Algebraic Computation, 1976, p. 136-148
26. Hanrot, G., and Zimmermann, P.: ' A long note on mulders' short product ', J. Symbol. Comput., 2004, 37, p. 391-401
27. Fan, H., and Hasan, M.A.: ' A new approach to subquadratic space complexity parallel multipliers for extended binary fields ', IEEE Trans. Comput., 2007, 56, (2), p. 224-233 0018-9340
28. n) multiplier for all trinomials ', IEEE Trans. Comput., 2005, 54, (4), p. 485-490 0018-9340
29. m) ', IEE Proc.-E, 1992, 139, (3), p. 230-236
30. Hasan, M.A., and Bhargava, V.K.: ' Architecture for low complexity rate-adaptive Reed-solomon encoder ', IEEE Trans. Comput., 1995, 44, (7), p. 938-942 0018-9340
31. Winograd, S.: ' Arithmetic complexity of computations ', SIAM, 1980
32. ' Table of low-weight binary irreducible polynomials ', Hewlett-Packard Laboratories, Palo Alto, California, 1998, [Online]. Available at: http://www.hpl.hp.com/techreports/98/HPL-98-135.html
33. m) ', Acta Appl. Math.: Int. Survey J. Appl. Math. Math. Appl., 2006, 93, (1-3), p. 33-55
34. k) using trinomial residue arithmetic ', Proc. 17th IEEE Symp. on Computer Arithmetic (ARITH 2005), June, 2005, p. 164-171