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Polynomials / Algebraic geometry / Commutative algebra / Computer algebra / System of polynomial equations / Finite field / NP / Time complexity / Elliptic curve only hash / Abstract algebra / Mathematics / Algebra


Document Date: 2015-04-21 04:05:40


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3SAT / Information Security Group / Renault / Information Securty Laboratory / /

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Product Issues / Product Recall / /

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Institute of Systems / Kyushu University / Institute of Mathematics / University College London / National Institute of Information / /

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cryptanalysis applications / polynomial systems / elaborate index calculus algorithms / Index calculus algorithms / exponential-time algorithms / index calculus algorithm / particular / relation search amounts / polynomial time algorithm / descent systems / relation search / generated systems / elimination algorithms / particular systems / obner basis algorithms / basis algorithms / generic algorithms / generic systems / multiplicative / random systems / /

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First fall / /

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Institute of Mathematics for Industry / Kyushu University / University College London / National Institute of Information and Communications Technology / Institute of Systems / Information Technologies and Nanotechnologies / Institute of Systems / /

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Petit / /

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hb / first author / second author / /

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solution / /

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previous algorithm / exponential-time algorithms / cryptography / following algorithm / Gr¨ obner basis algorithms / polynomial time algorithm / Index calculus algorithms / index calculus algorithm / 4.3 Binary DLP Algorithm / use block Gaussian elimination algorithms / DLP algorithms / resulting system using Gr¨obner basis algorithms / previous binary ECDLP algorithms / DLP algorithm / binary ECDLP Algorithms / DLP / 2 2.1 Preliminaries Gr¨ obner Basis Algorithms / elaborate index calculus algorithms / Gr¨obner basis algorithms / 4.1 Binary ECDLP Algorithm / BSGS algorithms / 2/3 algorithm / two algorithms / /

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