New Constructions and Applications of Trapdoor DDH Groups

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Provided by: ANSSI
Topic: Security
Format: PDF
Trapdoor Decisional Diffie-Hellman (TDDH) groups, introduced by the researchers (ANTS 2006), are groups where the DDH problem is hard, unless one is in possession of a secret trapdoor which enables solving it efficiently. Despite their intuitively appealing properties, they have found up to now very few cryptographic applications. Moreover, among the two constructions of such groups proposed by researchers, only a single one based on hidden pairings remains unbroken. In this paper, the authors extend the set of trapdoor DDH groups by giving a construction based on composite residuosity.
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