Unfortunately, De Mulder et al. [27] showed that the perturbation procedures and
random equation calculations can be separated from the implementation, and the linear
input and output encodings can be removed. Accordingly, attackers can transform the
white-box implementation into a simple but functional ly equivalent implementation
and then retrieve a set of keys that are equivalent to the original key. The cryptanalysis
of the white-box AES in [20] has a worst-case work factor of 2
17
.
Xiao et al. [15] proposed a white-box AES implementation after a detailed analysis
of attack techniques in [24]. The size of this implementation is considerably large to
achieve a higher security level. In Xi ao et al.’s scheme, the obfuscation works on at
least two cells of an AES stat e; moreover, the attacker cannot divide it into smaller
units (e.g. one cell of an AES state) and remove it using the attack techniques proposed
in [24]. The time complexity of the Xiao-Lai white-box AES implementation is 2
24
,
which is slower than the Chow et al.’ s implementation in [3](2
20
), and the size is
20502 KB.
De Mulder et al. [28] presented a practical cryptanalysis of Xiao et al.’s white-box
AES. They applied the linear equivalence algorithm presented by Biryukov et al. [29]
as a building block in their key-extraction algorithm. The cryptanalysis efficiently
extracts the AES key with a work factor of about 2
32
.
Another white-box implementation for AES is proposed by Karroumi [19]. This
implementation makes InvSubBytes and InvMixColumns operations variable by using
additional sets of coefficients taken from dual representations of AES. Karroumi
claimed that the expected security level is raised from 2
30
to 2
91
. However, an algebraic
analysis [30] was proposed in 2013 and Karroumi’s implementation can be easily
broken.
The two key factors of a white-box encryption algorithm are size and security level.
Unfortunately, in many cases, the two key facto rs form a tradeoff and cannot be
achieved simultaneously. The goal of light-weight WBEAs proposed in prior work
[16, 17] is to make the size of imp lementations as small as possible in order to meet the
requirements on computin g with mobile agents and sensor nodes. In general, these
white-box implementations only intend to support time-limited black box security [31].
As summarized in Table 1, white-box implementations designed for providing long
term protections (i.e., heavy-weight WBEAs) are listed in the left column with the
corresponding attacks listed in the right column. The latest published heavy-weight
WBEA (i.e., the white-box SHARK [5]) is also incl uded.
3 SHARK and its White-Box Implementation
SHARK [32] is a six round substitution-permutation-network that alternates a key
mixing stage with linear and non-linear transformation layers. Eac h round of the
SHARK encryption algorithm can be split into three distinct layers: a non-linear
confusion layer of S-Boxes, a linear diffusion layer and a key addition (XOR) layer.
Let S : GFð2
8
Þ!GFð2
8
Þ; x 7! S½x be the mapping of S-Boxes. Then the
substitution layer can be defined as c : GFð2
8
Þ
8
! GFð2
8
Þ
8
, cðaÞ¼b , b
i
¼ S½a
i
,
0 i 7.
458 Y. Shi and H. Fan
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