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In a seminal paper of identity based encryption (IBE), Boneh and Franklin [6] mentioned an interesting transform from an IBE scheme to a signature scheme, which was observed by Moni Naor. In this paper, we give formal security treatments for this transform and discover several implications and separations among security notions of IBE and transformed signature. For example, we show for such a successful transform, one-wayness of IBE is an essential condition. Additionally, we give a sufficient and necessary condition for converting a semantically secure IBE scheme into an existentially unforgeable signature scheme. Our results help establish strategies on design and automatic security proof of signature schemes from (possibly weak) IBE schemes. We also show some separation results which strongly support that one-wayness, rather than semantic security, of IBE captures an essential condition to achieve secure signature.

Formal Security Treatments for IBE-to-Signature Transformation: Relations among Security Notions