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- W2020012988 abstract "For symmetric pairings $e : mathbb{G} times mathbb{G} rightarrow mathbb{G}_T$, Verheul provedthat the existence of an efficiently-computable isomorphism $phi : mathbb{G}_Trightarrow mathbb{G}$ implies that the Diffie-Hellman problems in $mathbb{G}$ and $mathbb{G}_T$can be efficiently solved. In this paper, we explore the implications ofthe existence of efficiently-computable isomorphisms $phi_1 : mathbb{G}_Trightarrow mathbb{G}_1$ and $phi_2 : mathbb{G}_T rightarrow mathbb{G}_2$ for asymmetricpairings $e : mathbb{G}_1 times mathbb{G}_2 rightarrow mathbb{G}_T$. We also give a simplifiedproof of Verheul's theorem." @default.
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- W2020012988 date "2013-01-01" @default.
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- W2020012988 title "Generalizations of Verheul's theorem to asymmetric pairings" @default.
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- W2020012988 doi "https://doi.org/10.3934/amc.2013.7.103" @default.
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