Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms

We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group 𝐆$\mathbf {G}$. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bou...
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Autor*in:	Bos Joppe W. [verfasserIn] Dudeanu Alina [verfasserIn] Jetchev Dimitar [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	pollard rho additive walk collision bound random walk mixing times 94a60 05c81

Übergeordnetes Werk:	In: Journal of Mathematical Cryptology - De Gruyter, 2020, 8(2014), 1, Seite 71-92
Übergeordnetes Werk:	volume:8 ; year:2014 ; number:1 ; pages:71-92

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.1515/jmc-2012-0032

Katalog-ID:	DOAJ013306693

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520			\|a We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group $\mathbf {G}$. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bounds differ from the birthday bound (\| \|)$\mathcal {O}(\sqrt{\vert \mathbf {G}\vert })$ by a factor of log\| \|$\sqrt{\log {\vert \mathbf {G}\vert }}$ and are based on mixing time estimates for random walks on finite abelian groups due to Dou and Hildebrand.
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allfieldsSound	10.1515/jmc-2012-0032 doi (DE-627)DOAJ013306693 (DE-599)DOAJa8a71bc77d154ecfa5c52c572a4c1ff6 DE-627 ger DE-627 rakwb eng QA1-939 Bos Joppe W. verfasserin aut Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group 𝐆$\mathbf {G}$. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bounds differ from the birthday bound 𝒪(\|𝐆\|)$\mathcal {O}(\sqrt{\vert \mathbf {G}\vert })$ by a factor of log\|𝐆\|$\sqrt{\log {\vert \mathbf {G}\vert }}$ and are based on mixing time estimates for random walks on finite abelian groups due to Dou and Hildebrand. pollard rho additive walk collision bound random walk mixing times 94a60 05c81 Mathematics Dudeanu Alina verfasserin aut Jetchev Dimitar verfasserin aut In Journal of Mathematical Cryptology De Gruyter, 2020 8(2014), 1, Seite 71-92 (DE-627)527640387 (DE-600)2278189-4 18622984 nnns volume:8 year:2014 number:1 pages:71-92 https://doi.org/10.1515/jmc-2012-0032 kostenfrei https://doaj.org/article/a8a71bc77d154ecfa5c52c572a4c1ff6 kostenfrei https://doi.org/10.1515/jmc-2012-0032 kostenfrei https://doaj.org/toc/1862-2976 Journal toc kostenfrei https://doaj.org/toc/1862-2984 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2014 1 71-92
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source	In Journal of Mathematical Cryptology 8(2014), 1, Seite 71-92 volume:8 year:2014 number:1 pages:71-92
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author	Bos Joppe W.
spellingShingle	Bos Joppe W. misc QA1-939 misc pollard rho misc additive walk misc collision bound misc random walk misc mixing times misc 94a60 misc 05c81 misc Mathematics Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms
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topic_title	QA1-939 Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms pollard rho additive walk collision bound random walk mixing times 94a60 05c81
topic	misc QA1-939 misc pollard rho misc additive walk misc collision bound misc random walk misc mixing times misc 94a60 misc 05c81 misc Mathematics
topic_unstemmed	misc QA1-939 misc pollard rho misc additive walk misc collision bound misc random walk misc mixing times misc 94a60 misc 05c81 misc Mathematics
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title	Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms
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title_sort	collision bounds for the additive pollard rho algorithm for solving discrete logarithms
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title_auth	Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms
abstract	We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group 𝐆$\mathbf {G}$. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bounds differ from the birthday bound 𝒪(\|𝐆\|)$\mathcal {O}(\sqrt{\vert \mathbf {G}\vert })$ by a factor of log\|𝐆\|$\sqrt{\log {\vert \mathbf {G}\vert }}$ and are based on mixing time estimates for random walks on finite abelian groups due to Dou and Hildebrand.
abstractGer	We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group 𝐆$\mathbf {G}$. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bounds differ from the birthday bound 𝒪(\|𝐆\|)$\mathcal {O}(\sqrt{\vert \mathbf {G}\vert })$ by a factor of log\|𝐆\|$\sqrt{\log {\vert \mathbf {G}\vert }}$ and are based on mixing time estimates for random walks on finite abelian groups due to Dou and Hildebrand.
abstract_unstemmed	We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group 𝐆$\mathbf {G}$. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bounds differ from the birthday bound 𝒪(\|𝐆\|)$\mathcal {O}(\sqrt{\vert \mathbf {G}\vert })$ by a factor of log\|𝐆\|$\sqrt{\log {\vert \mathbf {G}\vert }}$ and are based on mixing time estimates for random walks on finite abelian groups due to Dou and Hildebrand.
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title_short	Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms
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score	7.402011

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Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms

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