6 B. SUN ET AL.
Definition 2.6 (Range Query): For a table T
A
andaninterval(a, b), the range query on T
A
can be defined as:
σ
a<A
i
<b
(T
A
) ={t|t ∈ T
A
and a < t(A
i
)<b}
where t (A
i
) is the value of tuple t on attribute A
i
and (a, b) is an interval of values taken
on attribute A
i
. Range query expands the querying capabilities by enabling the selection of
data that falls within a specific numerical or chronological range.
Definition 2.7 (Aggregation): For a table T
A
, an aggregation operation with respect to an
aggregate function f over attribute A
i
can be defined as:
α
f(A
i
)
(T
A
) = f
(
t(A
i
)|t ∈ T
A
)
where f could be SUM, COUNT, AVG, MIN, or MAX, and it computes a single value from the
set of A
i
values across all tuples t in T
A
.
Definition 2.8 (String Pattern Match): For a table T
A
and a pattern string P, the string
pattern match query can be defined as:
σ
A
i
LIKE P
(T
A
) ={t|t ∈ T
A
and P matches t(A
i
)}
where t(A
i
) is the string value of tuple t on attribute A
i
, and the pattern match is based on
SQL’s LIKE operator, which may include wildcard characters.
2.3.2. Security
We first define three aspects of security: data confidentiality, query privacy, data, and pro-
gram obliviousness. Additionally, we demonstrate the corresponding risks under security
definitions, including data leakages and attacks, and outline the security goals to address
these issues.
(1) Confidentiality.
Data confidentiality protects data from unauthorised access and disclosure, including
means for protecting personal privacy and proprietary information. We refer to the adaptive
security definition given by Curtmola et al. (2006) and use the leakage profile to define the
security.
Definition 2.9 (Confidentiality): Let = (KeyGen,EDBSetup,QueryExec,Dec) be a secure
SQL query scheme and L be a leakage function. For an efficient adversary A and a simulator
S, we define the experiments Real
A
and Ideal
A,S
as follows.
• Real
A
: A chooses where λ is a security parameter. The game runs EDBSetup and gives
EDB to A. Then A chooses a series of query q
1
, ..., q
m
. For all i ∈ [m], the game runs
QueryExec(EDB, q
i
) and gives output to A. Eventually, A outputs a bit b whichisalsothe
output of the Real
A
.
• Ideal
A,S
: A chooses DB. The simulator S initialises a query list q. The game runs EDB ←
S(L(DB)) and gives EDB to A. Then A chooses a series of query q
1
, ..., q
m
. For all i ∈ [m],
the game runs
S(L(DB, q
i
)) and gives output to A. Eventually, A outputs a bit b.
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