520 M. Qiu et al. / Journal of Computer and System Sciences 79 (2013) 518–529
full use of the slack time to incorporate security overhead into the process of scheduling tasks. Moreover, conventional
scheduling algorithms lack the capability to generate the optimal security strategy.
Recently, integrating cryptographic algorithms into ubiquitous real-time applications has received more attention. In [3],
Xie et al. proposed a Security-Aware Scheduling Algorithm (SASES) to improve the security of embedded system applications
composed of independent periodic tasks. The SASES algorithm is a heuristic algorithm based on the dynamic scheduling
algorithm EDF. It cannot guarantee predictability and optimality of the security strategy. In [14], Xie et al. proposed a task
allocation scheme named TPADPS to maximize the security quality and schedulability for real-time applications with task
dependence. In [4], Lin and Yang proposed an ILP model to solve the static schedulability driven security optimization
problem. Their method can only be applied to applications with independent periodic tasks.
In order to achieve the maximal system security strength and to guarantee the real-time schedulability, two critical
issues, i.e., quantitative security strength and computational overhead models, need to be solved. Researchers have worked
on quantitative measurements of the security strength of various cryptographic algorithms. Irvine and Levin [13] proposed a
security taxonomy and overhead framework. Xie et al. also proposed overhead models [12] that can approximately measure
security overheads experienced by tasks with security requirements. They mainly considered the security overhead model
for three types of basic and widely deployed security services: confidentiality, integrity, and authentication. The security
strength of various algorithms is quantized as quantitative security levels.
Similar to the level-based security model, Yang et al. [4] proposed a group based security model. They assume that the
system has different services with different quality. In [14] and [4], the overall system security strength is a weighted sum
of security strength of selected security algorithms. Note that how to accurately express the overall security strength is still
a challenge and open issue.
In this paper, we propose to use the risk-free probability to measure the security strength of each security algorithm.
Thereby, the overall strength of a security strategy is the product of these probability values.
3. Basic models and definitions
In this section, first we introduce the basic models which will be used in the later sections. Then, we formally define the
security optimization problem in this paper.
3.1. Security-aware task graph model
A large number of ubiquitous applications are implemented in a periodic manner, in which a set of tasks are executed
periodically. Previous literature uses independent task models to study the real-time scheduling problem [3,4].However,the
precedence relationship among tasks must be taken into account in many real applications. For example, in a video monitor
system, video signal capture, coding, compression, and transition are set of dependent tasks and executed in an identical
period.
In this paper, we propose the SEAT graph model to specify a real-time ubiquitous application. The precedence relationship
among tasks can be represented by directed edges of a SEAT graph. Security requirements and timing constraints can be
regarded as attributes of task nodes. The formal definition of the SEAT graph model is stated as follows.
Definition 3.1 (Security-aware task graph). ASEATG
=V , E, L, a(v) is a directed graph, where V is a set of tasks, E ⊆ V × V
is a set of edges that define the precedence relationships among task nodes in V , L represents the deadline of a single
iteration of the SEAT, a
(v) ={t(v), d(v), s
v
} is the attribute vector of task v, where t(v) denotes the execution time of
task v, d
(v) denotes the amount of data (measured in KB) that needs security protection, s
v
={s
1
v
, s
2
v
,...,s
n
v
} is the security
vector of task v,thevalueofs
i
v
represents the security requirement of the ith security service for task v.
We assume that all tasks in a SEAT have the same rate, i.e. the period of each task is identical. Therefore, the real-
time requirement can be guaranteed via deadline L.Anedgee
(v
i
→ v
j
) in E denotes that task v
j
cannot be executed
until task v
i
is completed. Note that in a SEAT the value of s
i
v
of the security vector s
v
is only the lower bound security
requirement of the ith security service for task v. In the next section, we present a general model to formulate the security
level of the application.
3.2. Security model
The security of a ubiquitous system is an ability of a system to withhold various attacks. The overall system secu-
rity strategy is composed of diverse security services such as data integrity, confidentiality, and authentication. And each
security service can be implemented by different cryptographic algorithms which lead to different security strength and
computational overhead.
For example, data confidentiality can be implemented by RC4 and AES cryptographic algorithms. RC4 is a very fast
algorithm since it uses only 7 CPU clock cycles per byte of output on a Pentium CPU architecture [18]. The memory space
cost of RC4 is also very low, say only 256 bytes of RAM. Hence, it was one of the best encryption schemes of the past
decade. However, Fluhrer et al. have discovered several vulnerabilities in the RC4 algorithm [19] that make it unsafe for
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