The cryptographic protocol known as the combined scheme allows users to
decrypt ciphertexts and create signatures using the same key.
In this paper, we model ID-based combined schemes.
Many ID-based encryption schemes and ID-based signature schemes
are proposed. Most of them are based on bilinear maps. 
Although it seems possible to combine these schemes,
there is no security definition for the combination.
We propose a model for this combinations, and define the security condition.
As an additional property, a definition for the key privacy of encryption schemes is proposed.
In the combined scheme, the same private key is used for the decryption and the signing.
To protect the owner's privacy,
both the encryption scheme and the signature scheme
must satisfy the key privacy condition.
When combining them, the encryption scheme should not
degrade the key privacy of the signature scheme, and vice versa.
We propose a key privacy condition for ID-based signature schemes.
We then modify this notion to ID-based combined schemes.
We construct a concrete scheme and prove that this scheme satisfies
these security requirements.
Furthermore, we discuss several related topics.
First, we propose a definition for the key privacy of a non-ID-based combined scheme, 
and prove that the prior scheme satisfies this property with a short modification.
We also propose an ID-based combined scheme with multiple-receiver encryption scheme. 
We prove the security of this concrete scheme.