A formal security proof of generic construction of anonymous IBE from PEKS

Abstract

Abdalla et al.[1, 2] proposed a transform of an anonymous IBE (A-IBE) scheme to a PEKS(Public
key encryption with keyword search) scheme. Boneh et al. proposed a transform of a PEKS scheme
to an A-IBE scheme for only one-bit message. Rhee et al.[3] proposed a transform for constructing
an A-IBE scheme for polynomially many-bit message by using a PEKS scheme. They firstly defined
a multiple PEKS (mPEKS) scheme and showed that a mPEKS scheme can be constructed from a
PEKS scheme. In this paper, we formally prove that if a PEKS scheme is confidential, so is the
resulting mPEKS scheme. We then provide a transform from a mPEKS scheme to an A-IBE scheme
for a polynomially many-bit message.