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Volumn 29, Issue 1, 2013, Pages 53-75

On the complexity of solving quadratic Boolean systems

Author keywords

Boolean quadratic system; Complexity; Gr bner bases; Multivariate cryptography; Semi regularity

Indexed keywords

BOOLEAN FUNCTIONS; CRYPTOGRAPHY; LINEAR ALGEBRA;

EID: 84870383684     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2012.07.001     Document Type: Article
Times cited : (71)

References (42)
  • 4
    • 33746062308 scopus 로고    scopus 로고
    • On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations
    • M. Bardet, J.-C. Faugère, B. Salvy, On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations, in: Proceedings of the International Conference on Polynomial System Solving, ISCPP, 2004, pp. 71-74.
    • (2004) Proceedings of the International Conference on Polynomial System Solving, ISCPP , pp. 71-74
    • M. Bardet1
  • 16
    • 0033143274 scopus 로고    scopus 로고
    • A new efficient algorithm for computing Gröbner bases (F4)
    • J.-C. Faugère A new efficient algorithm for computing Gröbner bases (F4) Journal of Pure and Applied Algebra 139 1-3 1999 61 88
    • (1999) Journal of Pure and Applied Algebra , vol.139 , Issue.13 , pp. 61-88
    • Faugère, J.-C.1
  • 18
    • 25944479355 scopus 로고
    • Efficient computation of zero-dimensional Gröbner bases by change of ordering
    • J.-C. Faugère, P. Gianni, D. Lazard, and T. Mora Efficient computation of zero-dimensional Gröbner bases by change of ordering Journal of Symbolic Computation 16 4 1993 329 344
    • (1993) Journal of Symbolic Computation , vol.16 , Issue.4 , pp. 329-344
    • Faugère, J.-C.1    Gianni, P.2    Lazard, D.3    Mora, T.4
  • 20
    • 77954636190 scopus 로고    scopus 로고
    • Algebraic cryptanalysis of McEliece variants with compact keys
    • Lecture Notes in Computer Science Springer-Verlag
    • J.-C. Faugère, A. Otmani, L. Perret, and J.-P. Tillich Algebraic cryptanalysis of McEliece variants with compact keys Advances in Cryptology - Eurocrypt 2010 Lecture Notes in Computer Science vol. 6110 2010 Springer-Verlag 279 298
    • (2010) Advances in Cryptology - Eurocrypt 2010 , vol.6110 , pp. 279-298
    • Faugère, J.-C.1    Otmani, A.2    Perret, L.3    Tillich, J.-P.4
  • 22
    • 0001908618 scopus 로고
    • Complexity of problems in games, graphs and algebraic equations
    • A.S. Fraenkel, and Y. Yesha Complexity of problems in games, graphs and algebraic equations Discrete Applied Mathematics 1 1-2 1979 15 30
    • (1979) Discrete Applied Mathematics , vol.1 , Issue.12 , pp. 15-30
    • Fraenkel, A.S.1    Yesha, Y.2
  • 23
    • 0001511869 scopus 로고
    • An inequality for Hilbert series of graded algebras
    • R. Fröberg An inequality for Hilbert series of graded algebras Mathematica Scandinavica 56 1985 117 144
    • (1985) Mathematica Scandinavica , vol.56 , pp. 117-144
    • Fröberg, R.1
  • 26
    • 24944453170 scopus 로고    scopus 로고
    • On the effective Nullstellensatz
    • DOI 10.1007/s00222-004-0434-8
    • Z. Jelonek On the effective Nullstellensatz Inventiones Mathematicae 162 1 2005 1 17 (Pubitemid 41312595)
    • (2005) Inventiones Mathematicae , vol.162 , Issue.1 , pp. 1-17
    • Jelonek, Z.1
  • 28
    • 84957693117 scopus 로고    scopus 로고
    • Unbalanced oil and vinegar signature schemes
    • Lecture Notes in Computer Science
    • A. Kipnis, J. Patarin, and L. Goubin Unbalanced oil and vinegar signature schemes Advances in Cryptology - Eurocrypt'99 Lecture Notes in Computer Science vol. 1592 1999 206 222
    • (1999) Advances in Cryptology - Eurocrypt'99 , vol.1592 , pp. 206-222
    • Kipnis, A.1    Patarin, J.2    Goubin, L.3
  • 29
    • 84957060922 scopus 로고    scopus 로고
    • Cryptanalysis of the HFE public key cryptosystem by relinearization
    • Lecture Notes in Computer Science Springer
    • A. Kipnis, and A. Shamir Cryptanalysis of the HFE public key cryptosystem by relinearization Advances in Cryptology - Crypto'99 Lecture Notes in Computer Science vol. 1666 1999 Springer 19 30
    • (1999) Advances in Cryptology - Crypto'99 , vol.1666 , pp. 19-30
    • Kipnis, A.1    Shamir, A.2
  • 31
    • 0037447691 scopus 로고    scopus 로고
    • Degrevlex Gröbner bases of generic complete intersections
    • DOI 10.1016/S0022-4049(02)00297-9, PII S0022404902002979
    • G. Moreno-Socías Degrevlex Gröbner bases of generic complete intersections Journal of Pure and Applied Algebra 180 3 2003 263 283 (Pubitemid 36379669)
    • (2003) Journal of Pure and Applied Algebra , vol.180 , Issue.3 , pp. 263-283
    • Moreno-Socias, G.1
  • 32
    • 84947932132 scopus 로고    scopus 로고
    • Hidden fields equations (HFE) and isomorphisms of polynomials (IP): Two new families of asymmetric algorithms
    • J. Patarin Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms Advances in Cryptology - Eurocrypt'96 Lecture Notes in Computer Science vol. 1070 1996 Springer 33 48 (Pubitemid 126071052)
    • (1996) Lecture Notes in Computer Science , Issue.1070 , pp. 33-48
    • Patarin, J.1
  • 33
    • 51349154683 scopus 로고    scopus 로고
    • On solving sparse algebraic equations over finite fields
    • I. Semaev On solving sparse algebraic equations over finite fields Designs, Codes and Cryptography 49 1-3 2008 47 60
    • (2008) Designs, Codes and Cryptography , vol.49 , Issue.13 , pp. 47-60
    • Semaev, I.1
  • 34
    • 67650118825 scopus 로고    scopus 로고
    • Sparse algebraic equations over finite fields
    • I. Semaev Sparse algebraic equations over finite fields SIAM Journal on Computing 39 2 2009 388 409
    • (2009) SIAM Journal on Computing , vol.39 , Issue.2 , pp. 388-409
    • Semaev, I.1
  • 35
    • 84870353804 scopus 로고
    • The probability that a linear system is consistent
    • E.L. Stitzinger The probability that a linear system is consistent Linear and Multilinear Algebra 21 4 1987 367 371
    • (1987) Linear and Multilinear Algebra , vol.21 , Issue.4 , pp. 367-371
    • Stitzinger, E.L.1
  • 40
  • 41
    • 33646770907 scopus 로고    scopus 로고
    • Theoretical analysis of XL over small fields
    • Lecture Notes in Computer Science
    • B.-Y. Yang, and J.-M. Chen Theoretical analysis of XL over small fields Information Security and Privacy 2004 Lecture Notes in Computer Science vol. 3108 2004 277 288
    • (2004) Information Security and Privacy 2004 , vol.3108 , pp. 277-288
    • Yang, B.-Y.1    Chen, J.-M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.