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sent to the cloud along with the LSSS matrix. A secure channel like ssh can
be used for the transmission.
We consider the example from Reference 31 of a network in which owners
want to store their data in encrypted form in the cloud and give selective
access to users. In a health care scenario, owners can be the patients who
store their records in the cloud, and doctors, nurses, researchers, and insur-
ance companies can retrieve them. There are attribute authorities, which
are servers scattered in different countries, that generate secret keys for the
users. AAs can be government organizations that give different credentials
to users. These servers can be maintained by separate companies, so that
they do not collude with each other. This differs from the concept of a cloud.
A particular cloud is maintained by one company; thus, if authorities are a
part of the cloud, then they can collude and find the secret keys of all the
users. Figure  3.1 shows the overall model of our cloud environment. The
users and owners are denoted by n i ; the AAs are servers that distribute attri-
butes and secret keys SK to users and owners. AAs are not part of the cloud.
The owner encrypts a message and stores the ciphertext C in the cloud.
Suppose an owner U u wants to store a record M . U u defines the access struc-
ture A, which helps it to decide the authorized set of users who can access
the record M . It then creates an m × h matrix R ( m is the number of attributes
in the access structure) and defines a mapping function π of its rows with the
attributes. π is a permutation, such that π :{1, 2, … , m } → W. The encryption
algorithm takes as input the data M that need to be encrypted, the group G ,
the LSSS matrix R , and the permutation function π, which maps the attributes
CT
CT
KDC 1
User n A
PK 2 , SK 2B
User n B
KDC 2
FIGURE 3.1
Distributed access control in clouds.
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