Idea Functionality is the core and basic unit of Universally Composable (UC) security protocols.The first step of designing the protocols

within the UCsecurity framework

is to extract an ideal functionality from the expected functionalities of the protocols.To appropriately define an ideal functionality we should not only protect the security of the definition

but also consider the realizability.This study investigates the security of identity-based signature (IBS) within the UCframework

defines a realizable identity-based signature functionality

F

IBS

proves that UC-secure IBS is equivalent to conventionally-secure (EUF-CMIA -secure) IBS.As a result

we are able to make sure that the EUF-CMIA scheme can be a module in designing a complex protocol that satisfies the UCrequirement.