메뉴 건너뛰기




Volumn 5984 LNCS, Issue , 2010, Pages 87-100

MXL3: An efficient algorithm for computing Gröbner bases of zero-dimensional ideals

Author keywords

Gr bner basis; Multivariate polynomial systems; Mutant; MutantXL algorithm; XL algorithm

Indexed keywords

EFFICIENT ALGORITHM; MULTIVARIATE POLYNOMIAL; MULTIVARIATE POLYNOMIAL SYSTEMS; SUFFICIENT CONDITIONS; ZERO-DIMENSIONAL IDEAL;

EID: 77954565760     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-14423-3_7     Document Type: Conference Paper
Times cited : (32)

References (17)
  • 3
    • 67349265781 scopus 로고    scopus 로고
    • Polybori: A framework for gröbner-basis computations with boolean polynomials
    • Effective Methods in Algebraic Geometry
    • Brickenstein, M., Dreyer, A.: Polybori: A framework for gröbner-basis computations with boolean polynomials. Journal of Symbolic Computation 44(9), 1326-1345 (2009); Effective Methods in Algebraic Geometry
    • (2009) Journal of Symbolic Computation , vol.44 , Issue.9 , pp. 1326-1345
    • Brickenstein, M.1    Dreyer, A.2
  • 4
    • 0004054295 scopus 로고
    • Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal
    • PhD thesis, Mathematical Institute, University of Innsbruck, Austria, English translation in
    • Buchberger, B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal (An Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal). PhD thesis, Mathematical Institute, University of Innsbruck, Austria, 1965 (English translation in Journal of Symbolic Computation (2004)
    • (1965) Journal of Symbolic Computation
    • Buchberger, B.1
  • 6
    • 77649327985 scopus 로고    scopus 로고
    • Efficient algorithms for solving overdefined systems of multivariate polynomial equations
    • Preneel, B. (ed.) EUROCRYPT 2000. Springer, Heidelberg
    • Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392-407. Springer, Heidelberg (2000)
    • (2000) LNCS , vol.1807 , pp. 392-407
    • Courtois, N.1    Klimov, A.2    Patarin, J.3    Shamir, A.4
  • 11
    • 0033143274 scopus 로고    scopus 로고
    • A new efficient algorithm for computing Gröbner bases (F4)
    • Faugère, J.-C.: A new efficient algorithm for computing Gröbner bases (F4). Pure and Applied Algebra 139(1-3), 61-88 (1999)
    • (1999) Pure and Applied Algebra , vol.139 , Issue.1-3 , pp. 61-88
    • Faugère, J.-C.1
  • 14
    • 35248840150 scopus 로고    scopus 로고
    • Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases
    • Boneh, D. (ed.) CRYPTO 2003. Springer, Heidelberg
    • Faugère, J.-C., Joux, A.: Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44-60. Springer, Heidelberg (2003)
    • (2003) LNCS , vol.2729 , pp. 44-60
    • Faugère, J.-C.1    Joux, A.2
  • 15
    • 71549124018 scopus 로고    scopus 로고
    • Algebraic Attack on the MQQ Public Key Cryptosystem
    • Proceedings of the 8th International Conference on Cryptology And Network Security (CANS 2009), Kanazawa, Ishikawa, Japan, December 2009. Springer, Heidelberg to appear
    • Mohamed, M.S.E., Ding, J., Buchmann, J., Werner, F.: Algebraic Attack on the MQQ Public Key Cryptosystem. In: Proceedings of the 8th International Conference on Cryptology And Network Security (CANS 2009), Kanazawa, Ishikawa, Japan, December 2009. LNCS, Springer, Heidelberg (to appear, 2009)
    • (2009) LNCS
    • Mohamed, M.S.E.1    Ding, J.2    Buchmann, J.3    Werner, F.4
  • 16
    • 56749170583 scopus 로고    scopus 로고
    • MXL2: Solving Polynomial Equations over GF(2) using an Improved Mutant Strategy
    • Buchmann, J., Ding, J. (eds.) PQCrypto 2008. Springer, Heidelberg
    • Mohamed, M.S.E., Mohamed, W.S.A.E., Ding, J., Buchmann, J.: MXL2: Solving Polynomial Equations over GF(2) using an Improved Mutant Strategy. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 203-215. Springer, Heidelberg (2008)
    • (2008) LNCS , vol.5299 , pp. 203-215
    • Mohamed, M.S.E.1    Mohamed, W.S.A.E.2    Ding, J.3    Buchmann, J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.