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Volumn 3329, Issue , 2004, Pages 323-337

The XL-algorithm and a conjecture from commutative algebra

Author keywords

Algebraic attacks; Cryptanalysis; Extended linearization; Fr berg's Conjecture; Overdetermined systems of polynomial equations

Indexed keywords

ALGEBRA; COMPUTATION THEORY; CRYPTOGRAPHY; LINEARIZATION; POLYNOMIALS; SECURITY OF DATA;

EID: 24944450905     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-30539-2_23     Document Type: Article
Times cited : (62)

References (16)
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    • J.-M. Chen and B.-Y. Yang. Theoretical Analysis of XL over Small Fields. In H. Wang, J. Pieprzyk, V. Varadharajan, editors, Information Security and Privacy, volume 3108 of LNCS, pages 277-288, Springer-Verlag, Berlin, 2004.
    • (2004) LNCS , vol.3108 , pp. 277-288
    • Chen, J.-M.1    Yang, B.-Y.2
  • 5
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    • Higher Order Correlation Attacks, XL algorithm, and Cryptanalysis of Toyocrypt
    • P.J. Lee, C.H. Lim, editors, Advances in Cryptology -ICISC 02, Springer-Verlag, Berlin
    • N. Courtois. Higher Order Correlation Attacks, XL algorithm, and Cryptanalysis of Toyocrypt. In P.J. Lee, C.H. Lim, editors, Advances in Cryptology -ICISC 02, volume 2587 of LNCS, pages 182-199, Springer-Verlag, Berlin, 2002.
    • (2002) LNCS , vol.2587 , pp. 182-199
    • Courtois, N.1
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    • 77649327985 scopus 로고    scopus 로고
    • Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
    • B. Preneel, editor, Advances in Cryptology -EUROCRYPT 2000, Springer-Verlag, Berlin
    • N. Courtois, A. Klimov, J. Pararin, and A. Shamir. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In B. Preneel, editor, Advances in Cryptology -EUROCRYPT 2000, volume 1807 of LNCS, pages 392-407. Springer-Verlag, Berlin, 2000.
    • (2000) LNCS , vol.1807 , pp. 392-407
    • Courtois, N.1    Klimov, A.2    Pararin, J.3    Shamir, A.4
  • 8
    • 84958765510 scopus 로고    scopus 로고
    • Cryptanalysis of block ciphers with overdefined systems of equations
    • Y. Zheng, editor, Advances in Cryptology -ASIACRYPT 2002, Springer-Verlag, Berlin
    • N. Courtois and J. Pieprzyk. Cryptanalysis of block ciphers with overdefined systems of equations. In Y. Zheng, editor, Advances in Cryptology -ASIACRYPT 2002, volume 2501 of LNCS, pages 267-287. Springer-Verlag, Berlin, 2002.
    • (2002) LNCS , vol.2501 , pp. 267-287
    • Courtois, N.1    Pieprzyk, J.2
  • 10
    • 0001511869 scopus 로고
    • An inequality for Hubert series of graded algebras
    • R. Fröberg. An inequality for Hubert series of graded algebras. Math. Scand., 56:117-144, 1985.
    • (1985) Math. Scand. , vol.56 , pp. 117-144
    • Fröberg, R.1
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    • 0006511296 scopus 로고    scopus 로고
    • Problems and Results on Hubert Polynomials of Graded Algebras
    • J. Elas and J. Giral, editors, Six Lectures on Commutative Algebra, Birkhauser, Basel
    • G. Valla. Problems and Results on Hubert Polynomials of Graded Algebras. In J. Elas and J. Giral, editors, Six Lectures on Commutative Algebra, volume 166 of Progress in Mathematics. Birkhauser, Basel, 1996.
    • (1996) Progress in Mathematics , vol.166
    • Valla, G.1


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