11 Information Hiding for Spatial and Geographical Data
253
that own the right secret-key S K i will be able to retrieve both the digital map DM
and the sensitive content HC.
Let us describe both the Embed and the Extract functions in detail. These functions
are the core functions applied by the Embedding and the Extraction applications, respectively. Let us start with the Embed function that is illustrated in Table. 11.3. It
takes a digital map DM, the content HC that should be hidden in the digital map,
the secret-key of the Embedder S K E , and the public-key PK i of the class of users i
that will be authorized to visualize the hidden content. By applying the Embed DM ()
function, the digital map is stored in the GIS with the help of the secret-key of the
Embedder S K E , so that each user may verify and visualize it by applying the corresponding Extract DM () function with the public-key of the Embedder PK E that everyone knows. The resulting publicly available digital map is dm.
By applying the Embed HC () function, the sensitive content is hidden in the digital
map with the help of the public-key PK i of the class of users i that will be authorized
to visualize the hidden content. The secret content that will be available only to this
class of users is hc.
Then, the resulting stego-map is composed of dm and hc, and it may be transmitted to different users in a secure way. The security of this application is based
on the security of the public-key steganography method that is used to produce the
stego-map. Some security results were given in Sect. 11.2.3.
11.6.2 The Extraction Application
In this section, we introduce the Extraction application that is based on the Extract()
function, given in Table. 11.4.
The Extract() function takes a stego-map S M, the secret-key of a generic user
S K m , and the public-key PK i that was used by the Embedding application to embed the sensitive content in a digital map. The digital map may be visualized by
every user by extracting it from the stego-map. In fact, each user knows the publickey of the Embedder, so they can have access to the digital map dm. Also, if
they own the right secret-key, that is, the secret-key S K m associated to the publickey PK i in the key space K GEN , then, they will be authorized to have access to
Table 11.3. Embed is the core function of the Embedding application. It is used to create a
stego map that is composed of the digital map dm and some possible sensitive content hc that
is embedded inside dm with the public-key PK i of the class of authorized users
Procedure Embed
Input:
DM, HC, S K E , PK i ;
Embed DM (DM, S K E ) = dm;
Embed HC (DM, HC) PK i = hc;
S M = dm + hc;
Output: S M
253
that own the right secret-key S K i will be able to retrieve both the digital map DM
and the sensitive content HC.
Let us describe both the Embed and the Extract functions in detail. These functions
are the core functions applied by the Embedding and the Extraction applications, respectively. Let us start with the Embed function that is illustrated in Table. 11.3. It
takes a digital map DM, the content HC that should be hidden in the digital map,
the secret-key of the Embedder S K E , and the public-key PK i of the class of users i
that will be authorized to visualize the hidden content. By applying the Embed DM ()
function, the digital map is stored in the GIS with the help of the secret-key of the
Embedder S K E , so that each user may verify and visualize it by applying the corresponding Extract DM () function with the public-key of the Embedder PK E that everyone knows. The resulting publicly available digital map is dm.
By applying the Embed HC () function, the sensitive content is hidden in the digital
map with the help of the public-key PK i of the class of users i that will be authorized
to visualize the hidden content. The secret content that will be available only to this
class of users is hc.
Then, the resulting stego-map is composed of dm and hc, and it may be transmitted to different users in a secure way. The security of this application is based
on the security of the public-key steganography method that is used to produce the
stego-map. Some security results were given in Sect. 11.2.3.
11.6.2 The Extraction Application
In this section, we introduce the Extraction application that is based on the Extract()
function, given in Table. 11.4.
The Extract() function takes a stego-map S M, the secret-key of a generic user
S K m , and the public-key PK i that was used by the Embedding application to embed the sensitive content in a digital map. The digital map may be visualized by
every user by extracting it from the stego-map. In fact, each user knows the publickey of the Embedder, so they can have access to the digital map dm. Also, if
they own the right secret-key, that is, the secret-key S K m associated to the publickey PK i in the key space K GEN , then, they will be authorized to have access to
Table 11.3. Embed is the core function of the Embedding application. It is used to create a
stego map that is composed of the digital map dm and some possible sensitive content hc that
is embedded inside dm with the public-key PK i of the class of authorized users
Procedure Embed
Input:
DM, HC, S K E , PK i ;
Embed DM (DM, S K E ) = dm;
Embed HC (DM, HC) PK i = hc;
S M = dm + hc;
Output: S M