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Volumn 4876 LNCS, Issue , 2007, Pages 173-183

Explicit formulas for efficient multiplication in double-struck F sign 36m

Author keywords

Fast fourier transform; Finite field arithmetic; Lagrange interpolation; Tate pairing computation

Indexed keywords

FAST FOURIER TRANSFORMS; INTERPOLATION; LAGRANGE MULTIPLIERS; PROBLEM SOLVING;

EID: 38549102459     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: None     Document Type: Conference Paper
Times cited : (22)

References (20)
  • 1
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    • Knuth, D.E.: The Art of Computer Programming. In: Seminumerical Algorithms, 3rd edn., vol. 2, Addison-Wesley, Reading MA (1998), First edition (1969)
  • 2
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    • von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 2nd edn. Cambridge University Press, Cambridge (2003), First edition (1999)
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  • 3
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    • Department, U.S.: of Commerce / National Institute of Standards and Technology: Digital Signature Standard (DSS), Federal Information Processings Standards Publication 186-2 (January 2000)
    • Department, U.S.: of Commerce / National Institute of Standards and Technology: Digital Signature Standard (DSS), Federal Information Processings Standards Publication 186-2 (January 2000)
  • 4
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    • Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
    • Krawczyk, H, ed, CRYPTO 1998, Springer, Heidelberg
    • Bailey, D.V., Paar, C.: Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 472-485. Springer, Heidelberg (1998)
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    • Bailey, D.V.1    Paar, C.2
  • 5
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    • Avanzi, R.M., Mihǎilescu, P.: Generic Efficient Arithmetic Algorithms for PAFFs (Processor Adequate Finite Fields) and Related Algebraic Structures (Extended Abstract. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, 3006, pp. 320-334. Springer, Heidelberg (2004)
    • Avanzi, R.M., Mihǎilescu, P.: Generic Efficient Arithmetic Algorithms for PAFFs (Processor Adequate Finite Fields) and Related Algebraic Structures (Extended Abstract. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol. 3006, pp. 320-334. Springer, Heidelberg (2004)
  • 6
    • 0345490614 scopus 로고    scopus 로고
    • Tate-Pairing Implementations for Tripartite Key Agreement
    • Laih, C.-S, ed, ASIACRYPT 2003, Springer, Heidelberg
    • Duursma, I., Lee, H.: Tate-Pairing Implementations for Tripartite Key Agreement. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 111-123. Springer, Heidelberg (2003)
    • (2003) LNCS , vol.2894 , pp. 111-123
    • Duursma, I.1    Lee, H.2
  • 7
    • 27244434197 scopus 로고    scopus 로고
    • Kerins, T., Marnane, W.P., Popovici, E.M., Barreto, P.S.L.M.: Efficient Hardware for the Tate Pairing Calculation in Characteristic Three. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, 3659, pp. 412-426. Springer, Heidelberg (2005)
    • Kerins, T., Marnane, W.P., Popovici, E.M., Barreto, P.S.L.M.: Efficient Hardware for the Tate Pairing Calculation in Characteristic Three. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 412-426. Springer, Heidelberg (2005)
  • 8
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    • Karatsuba, A., Ofman, Y.: Multiplication of Multidigit Numbers on Automata. Soviet Physics-Doklady 7(7), 595-596 (1963) Translated from Doklady Akademii Nauk SSSR 145(2), 293-294 (July 1962)
    • Karatsuba, A., Ofman, Y.: Multiplication of Multidigit Numbers on Automata. Soviet Physics-Doklady 7(7), 595-596 (1963) Translated from Doklady Akademii Nauk SSSR 145(2), 293-294 (July 1962)
  • 13
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    • Arithmetic Operations in Finite Fields of Medium Prime Characteristic Using the Lagrange Representation
    • Bajard, J.C., Imbert, L., Negre, C.: Arithmetic Operations in Finite Fields of Medium Prime Characteristic Using the Lagrange Representation. IEEE Transactions on Computers 55(9), 1167-1177 (2006)
    • (2006) IEEE Transactions on Computers , vol.55 , Issue.9 , pp. 1167-1177
    • Bajard, J.C.1    Imbert, L.2    Negre, C.3
  • 14
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    • Blahut, R.E.: Fast Algorithms for Digital Signal Processing. Addison-Wesley, Reading MA (1985)
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    • An Algorithm for the Machine Computation of the Complex Fourier Series
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  • 17
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    • 2. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, 3897, pp. 359-369. Springer, Heidelberg (2006)
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  • 18
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    • Five, Six, and Seven-Term Karatsuba-Like Formulae
    • Montgomery, P.L.: Five, Six, and Seven-Term Karatsuba-Like Formulae. IEEE Transactions on Computers 54(3), 362-369 (2005)
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  • 20
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    • p - x + d
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    • p - x + d. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 111-123. Springer, Heidelberg (2003)
    • (2003) LNCS , vol.2894 , pp. 111-123
    • Duursma, I.1    Lee, H.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.