4
(t
4
, Max]:
N
[0, t
4
]:
Y
(t
4
, Max]:
N
[0, t
4
]:
Y
(t
4
, Max]:
N
[0, t
4
]:
Y
(t
4
, Max]:
N
[0, t
4
]:
Y
(t
4
, Max]:
N
[0, t
4
]:
Y
(t
4
, Max]:
N
[0, t
4
]:
Y
(t
4
, Max]:
N
[0, t
4
]:
Y
[0, t
3
]:N
[0, t
3
]:N
(t
3
, Max]:Y
(t
3
, Max]:Y[0, t
3
]:N
(t
3
, Max]:Y
(t
3
, Max]:Y
[0, t
3
]:N
(t
1
, Max]: H[0, t
1
]: L
Systolic BP
[t
1
]
Missed
Medication [t
2
]
(t
2
, Max]:N
[0, t
2
]:Y
(t
2
, Max]:N
[0, t
2
]:Y
Missed
Medication [t
2
]
Physical Activity
[t
3
]
Physical Activity
[t
3
]
Physical Activity
[t
3
]
Physical Activity
[t
3
]
Normal Diet
[t
4
]
Normal Diet
[t
4
]
Normal Diet
[t
4
]
Normal Diet
[t
4
]
Normal Diet
[t
4
]
Normal Diet
[t
4
]
Normal Diet
[t
4
]
Normal Diet
[t
4
]
D
2
D
7
D
6
D
6
(t
4
, Max]:
N
[0, t
4
]:
Y
D
2
D
3
D
4
D
5
D
2
D
3
D
4
D
5
D
2
D
3
D
4
D
2
D
3
D
4
D
2
D
4
D
5
D
7
D
2
D
4
D
7
D
2
D
5
D
7
D
4
D
5
D
6
D
5
D
6
D
1
D
3
D
4
D
5
D
6
D
1
D
3
D
4
D
5
D
6
D
1
D
3
D
4
D
5
D
6
D
1
D
3
D
4
D
5
D
6
D
1
: Take extra medication
D
2
: Increase fluid intake
D
3
: Notify Physician
D
4
: Notify Next of Kin
D
5
: Modify daily diet
D
6
: Take regular medication
D
7
: Do not take next dosage of medication
Fig. 2. Using branching program to represent a real monitoring program in MediNet project
h = L(1), else h = R(1). Repeat the process recursively for
p
h
, and so on, until one of the leaf nodes is reached with
decision information.
To illustrate how a practical monitoring program can be
transformed into a branching program, we use the monitor-
ing program introduced in the MediNet project [32], [33]
to construct a branching program as shown in Fig. 2. The
MediNet aims to provide automatic personalized monitoring
service for patients with diabetes or cardiovascular diseases.
Clients input their related health data such as systolic blood
pressure (BP), whether they missed daily medications or had
an abnormal diet, and the energy consumption of physical
activity to the decision support system, which will then
return a recommendation on how the clients can improve
their conditions. For instance, assume a hypertension patient
inputs an attribute vector consisting of the following elements
“[Systolic BP: 150, Missed one medication=0 (indicating he
did miss the medication), Energy Expenditure: 900 kcal,
salt intake: 1000 milligrams]” and the respective threshold
is “t
1
= 130, t
2
= 0, t
3
= 700kcal, t
4
= 1500”. The
recommendation returned from the monitoring program (Fig.
2) would be “ D
4
, D
5
, D
6
” (by following the path through
comparing each attribute element with the respective threshold
at each node), which indicates the clients need to “notify
next kin, modify daily diet, and take regular medication”. The
health data related to the input attribute vector can be sampled
either by a portable sensor or input by the client.
S
[001, 100]
={001, 01, 100}
S
010
={ŏ, 0, 01, 010}
ŏ
ŏ
Fig. 3. Basic idea of MDRQ
C. Homomorphic encryption
Homomorphic encryption is widely used as an underlying
tool for constructing secure protocols in the literature [34],
[35]. CAM adopts a semantically secure additively homomor-
phic public-key encryption technique. Intuitively, for homo-
morphic encryption HEnc(·), given two encrypted messages
HEnc(m
1
) and HEnc(m
2
), the encryption of the addition of
the two underlying messages can be computed additively as
follows: HEnc(m
1
+m
2
) = HEnc(m
1
)⋆HEnc(m
2
), where ⋆ is
the corresponding operation in the ciphertext space. A typical
additively homomorphic encryption scheme was proposed by
Paillier cryptosystem [36], [37]. Homomorphic encryption
enables a client to obtain the token corresponding to the input
attribute vectors obliviously from TA.
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