Efficient FPGA-based Karatsuba multipliers for polynomials over F 2

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

Volumn 3897 LNCS, Issue , 2006, Pages 359-369

  Von Zur Gathen, Joachim ^a   Shokrollahi, Jamshid ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

Asymptotically fast algorithms; Fast multiplication; Finite field arithmetic; FPGA; Hardware; Karatsuba method

Indexed keywords

ADAPTIVE ALGORITHMS; COMPUTER AIDED DESIGN; COMPUTER HARDWARE; FINITE AUTOMATA; FREQUENCY MULTIPLYING CIRCUITS; INTEGRATED CIRCUIT LAYOUT; POLYNOMIALS;

ASYMPTOTICALLY FAST ALGORITHMS; FAST MULTIPLICATIONS; FINITE FIELD ARITHMETICS; KARATSUBA METHOD;

FIELD PROGRAMMABLE GATE ARRAYS;

EID: 33745686500     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11693383_25     Document Type: Conference Paper

References (15)

1. Bailey, D.V., Paar, C.: Optimal extension fields for fast arithmetic in publickey algorithms. In Krawczyk, H., ed.: Advances in Cryptology: Proceedings of CRYPTO '98, Santa Barbara CA. Number 1462 in Lecture Notes in Computer Science, Springer-Verlag (1998) 472-485
2. Blahut, R.E.: Fast Algorithms for Digital Signal Processing. Addison-Wesley, Reading MA (1985)
3. Cantor, D.G.: On arithmetical algorithms over finite fields. Journal of Combinatorial Theory, Series A 50 (1989) 285-300
4. 2. In Lakshman, Y.N., ed.: Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation ISSAC '96, Zürich, Switzerland, ACM Press (1996) 1-9 Technical report tr-rsfb-96-018, University of Paderborn, Germany, 1996, 43 pages. Final version in Mathematics of Computation.
5. von zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Second edn. Cambridge University Press, Cambridge, UK (2003) First edition 1999.
6. von zur Gathen, J., Nöcker, M.: Polynomial and normal bases for finite fields. Journal of Cryptology (2005) to appear.
7. 233 multipliers. In: Proc. of the IEEE International Symposium on Circuits and Systems (ISCAS-03). Volume II, Bangkok, Thailand (2003) 268-271
8. Hankerson, D., Menezes, A., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer-Verlag (2003)
9. n). In: Workshop on Cryptographic Hardware and Embedded Systems, Hamburg, IEEE (2002)
10. Karatsuba, A., Ofman, Y.: Multiplication of multidigit numbers on automata. Soviet Physics-Doklady 7 (1963) 595-596
11. translated from Doklady Akademii Nauk SSSR, Vol. 145, No. 2, pp. 293-294, July, 1962.
12. m). US Patent Application (2002)
13. Paar, C.: Efficient VLSI Architectures for Bit-Parallel Computation in Galois Fields. PhD thesis, Institute for Experimental Mathematics, University of Essen, Essen, Germany (1994)
14. U.S. Department of Commerce / National Institute of Standards and Technology: Digital Signature Standard (DSS). (2000) Federal Information Processings Standards Publication 186-2.
15. Weimerskirch, A., Paar, C.; Generalizations of the karatsuba algorithm for efficient implementations. Technical report, Ruhr-Universität-Bochum, Germany (2003)