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Identity-based cryptography (IBC) is an asymmetric key cryptographic technology with a special feature, in which a user's public key can be an identifier of the user and the corresponding private key is created by binding the identifier with a system master secret. This paper is based on the author's lecture notes in this area. In this paper, we introduce the concept of IBC by explaining some basic cryptographic primitives, such as identity-based encryption, signatures, combined encryption/ signing and key-agreement. We also introduce two types of implementation techniques, which are based on integer factorization and discrete logarithm from pairings respectively. In order to make the technology easier to understand, we describe a small number of mechanisms in each primitive. Some of the mechanisms have been adopted by international standard bodies. At the end of the paper, we briefly cover the key escrow issue and a few well-known security models for these primitives.