메뉴 건너뛰기




Volumn 26, Issue 2, 2010, Pages 172-186

On multiplication in finite fields

Author keywords

Algebraic function fields; Bilinear complexity; Finite fields

Indexed keywords

COMPUTATIONAL COMPLEXITY; NUMERICAL ANALYSIS;

EID: 77649339854     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2009.11.002     Document Type: Article
Times cited : (29)

References (29)
  • 3
    • 0037172915 scopus 로고    scopus 로고
    • Quasi-optimal algorithms for multiplication in the extension of degree 13, 14, and 15
    • Ballet S. Quasi-optimal algorithms for multiplication in the extension of degree 13, 14, and 15. Journal of Pure and Applied Algebra 171 (2002) 149-164
    • (2002) Journal of Pure and Applied Algebra , vol.171 , pp. 149-164
    • Ballet, S.1
  • 4
    • 1642437958 scopus 로고    scopus 로고
    • Multiplication algorithm in a finite field and tensor rank of the multiplication
    • Ballet S., and Rolland R. Multiplication algorithm in a finite field and tensor rank of the multiplication. Journal of Algebra 272/1 (2004) 173-185
    • (2004) Journal of Algebra , vol.272-1 , pp. 173-185
    • Ballet, S.1    Rolland, R.2
  • 6
    • 77649342908 scopus 로고    scopus 로고
    • On an application of the definition field descent of a tower of function filed
    • Colloque International Arithmetic, Geometry and Coding Theory 2005 (AGCT 10)
    • Ballet S., Le Brigand D., and Rolland R. On an application of the definition field descent of a tower of function filed. Colloque International Arithmetic, Geometry and Coding Theory 2005 (AGCT 10). Société Mathématiques de France, sér. Séminaires et Congrés vol. 21 (2009) 187-203
    • (2009) Société Mathématiques de France, sér. Séminaires et Congrés , vol.21 , pp. 187-203
    • Ballet, S.1    Le Brigand, D.2    Rolland, R.3
  • 7
    • 32644454131 scopus 로고    scopus 로고
    • An improvement of the construction of the D.V. and G.V. Chudnovsky algorithm for multiplication in finite fields
    • Ballet S. An improvement of the construction of the D.V. and G.V. Chudnovsky algorithm for multiplication in finite fields. Theoretical Computer Science 352 (2006) 293-305
    • (2006) Theoretical Computer Science , vol.352 , pp. 293-305
    • Ballet, S.1
  • 8
    • 43049087455 scopus 로고    scopus 로고
    • On the tensor rank of the multiplication in the finite fields
    • Ballet S. On the tensor rank of the multiplication in the finite fields. Journal of Number Theory 128 (2008) 1795-1806
    • (2008) Journal of Number Theory , vol.128 , pp. 1795-1806
    • Ballet, S.1
  • 9
    • 84862528696 scopus 로고    scopus 로고
    • A note on the tensor rank of the multiplication in certain finite fields
    • Algebraic Geometry and its Applications. Hirschfeld J., Chaumine J., and Rolland R. (Eds). (Proceedings of Symposium of Algebraic Geometry and Applications, Tahiti, 7-11 mai 2007), World Scientific
    • Ballet S. A note on the tensor rank of the multiplication in certain finite fields. In: Hirschfeld J., Chaumine J., and Rolland R. (Eds). Algebraic Geometry and its Applications. (Proceedings of Symposium of Algebraic Geometry and Applications, Tahiti, 7-11 mai 2007). Number Theory and its Applications vol. 5 (2008), World Scientific 332-342
    • (2008) Number Theory and its Applications , vol.5 , pp. 332-342
    • Ballet, S.1
  • 13
    • 45449109186 scopus 로고    scopus 로고
    • ℓ m , m ≥ 1 and 5 ≤ ℓ ≤ 18
    • Africacrypt 2008, Springer-Verlag
    • ℓ m , m ≥ 1 and 5 ≤ ℓ ≤ 18. Africacrypt 2008. Lecture Notes in Computer Science vol. 5023 (2008), Springer-Verlag 406-414
    • (2008) Lecture Notes in Computer Science , vol.5023 , pp. 406-414
    • Cenk, M.1    Özbudak, F.2
  • 14
    • 38249029470 scopus 로고
    • Algebraic complexities and algebraic curves over finite fields
    • Chudnovsky D.V., and Chudnovsky G.V. Algebraic complexities and algebraic curves over finite fields. Journal of Complexity 4 (1988) 285-316
    • (1988) Journal of Complexity , vol.4 , pp. 285-316
    • Chudnovsky, D.V.1    Chudnovsky, G.V.2
  • 15
    • 34147183153 scopus 로고    scopus 로고
    • Comments on five, six, and seven-term Karatsuba-like formulae
    • Fan H., and Hasan M.A. Comments on five, six, and seven-term Karatsuba-like formulae. IEEE Transactions on Computers 56 5 (2007) 716-717
    • (2007) IEEE Transactions on Computers , vol.56 , Issue.5 , pp. 716-717
    • Fan, H.1    Hasan, M.A.2
  • 16
    • 14844351609 scopus 로고    scopus 로고
    • 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 (2005) 362-369
    • (2005) IEEE Transactions on Computers , vol.54 , Issue.3 , pp. 362-369
    • Montgomery, P.L.1
  • 19
    • 0041832237 scopus 로고    scopus 로고
    • Constructions of digital nets using global function fields
    • Niederreiter H., and Özbudak F. Constructions of digital nets using global function fields. Acta Arithmetica 105 3 (2002) 279-302
    • (2002) Acta Arithmetica , vol.105 , Issue.3 , pp. 279-302
    • Niederreiter, H.1    Özbudak, F.2
  • 20
    • 56649094579 scopus 로고    scopus 로고
    • Improved asymptotoic bounds for codes using distinguished divisors of global function fields
    • Niederreiter H., and Özbudak F. Improved asymptotoic bounds for codes using distinguished divisors of global function fields. SIAM Journal on Discrete Mathematics 21 4 (2007) 865-899
    • (2007) SIAM Journal on Discrete Mathematics , vol.21 , Issue.4 , pp. 865-899
    • Niederreiter, H.1    Özbudak, F.2
  • 21
    • 35248887146 scopus 로고    scopus 로고
    • Hardware implementation of finite fields of characteristic three
    • CHESS 2003, Springer-Verlag pp. 539-539
    • Page D., and Smart N.P. Hardware implementation of finite fields of characteristic three. CHESS 2003. Lecture Notes in Computer Science vol. 2523 (2003), Springer-Verlag pp. 539-539
    • (2003) Lecture Notes in Computer Science , vol.2523
    • Page, D.1    Smart, N.P.2
  • 22
    • 0001608539 scopus 로고
    • Optimal algortihms for multiplication in certain finite fields using algebraic curves
    • Shokrollahi M.A. Optimal algortihms for multiplication in certain finite fields using algebraic curves. SIAM Journal on Computing 21 6 (1992) 1193-1198
    • (1992) SIAM Journal on Computing , vol.21 , Issue.6 , pp. 1193-1198
    • Shokrollahi, M.A.1
  • 23
    • 0142167280 scopus 로고
    • Curves with many points and multiplication in finite fields
    • Springer, Berlin
    • Shparlinski I.E., Tsfasman M.A., and Vladut S.G. Curves with many points and multiplication in finite fields. Lecture Notes in Mathematics vol. 1518 (1992), Springer, Berlin 145-169
    • (1992) Lecture Notes in Mathematics , vol.1518 , pp. 145-169
    • Shparlinski, I.E.1    Tsfasman, M.A.2    Vladut, S.G.3
  • 26
    • 77649341229 scopus 로고    scopus 로고
    • A. Weimerskirch, C. Paar, Generalizations of the Karatsuba algorithm for polynomial multiplication. Avaliable at: http://eprint.iacr.org/2006/224
    • A. Weimerskirch, C. Paar, Generalizations of the Karatsuba algorithm for polynomial multiplication. Avaliable at: http://eprint.iacr.org/2006/224
  • 28
    • 21844523415 scopus 로고
    • Low-discrepancy sequences obtained from algebraic function-fields over finite-fields
    • Xing C.P., and Niederreiter H. Low-discrepancy sequences obtained from algebraic function-fields over finite-fields. Acta Arithmetica 72 3 (1995) 281-298
    • (1995) Acta Arithmetica , vol.72 , Issue.3 , pp. 281-298
    • Xing, C.P.1    Niederreiter, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.