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A New Differential Fault Attack on SPN Structure, with Application to AES Cipher

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A New Differential Fault Attack on SPN Structure, with Application to AES Cipher 216 JOURNAL OF COMPUTERS, VOL. 6, NO. 2, FEBRUARY 2011 A New Differential Fault Attack on SPN Structure, with Application to AES Cipher Wei Li1,2, Xiaoling Xia1, Dawu Gu2, Zhiqiang Liu2, Juanru Li2, Ya Liu2 1School of Computer Science and Technology, Donghua University 2Department of Computer Science and Engineering, Shanghai Jiao Tong University Email: [email protected] Abstract—The Substitution-Permutation Network (SPN) is a In this paper we focus on one type of side-channel main type of structure in block ciphers. This paper proposes attacks, known as a Differential Fault Analysis (DFA) a new and practical differential fault attack technique on [6]. The DFA attack was first proposed in 1997 as an SPN structure. As an instance of SPN cipher, AES-256 can attack on DES [6]. Later the similar attacks have been be recovered by 4 faulty ciphertexts. Compared with the applied to AES [1, 3, 7-9, 11, 12], Triple-DES [13], RC4 previous techniques, our work can recover all subkeys of an SPN cipher with all key sizes. Therefore, our attacking [5, 19] etc. The DFA attack is based on deriving method on AES not only improves the efficiency of fault information about the secret key by examining the injection, but also decreases the number of faulty differences between a cipher resulting from a correct ciphertexts. It provides a new approach for fault analysis on operation and a cipher of the same initial message block ciphers. resulting from a faulty operation. A Substitution-Permutation Network (SPN) is a basic Index Terms—Cryptanalysis, Side channel attacks, structure, which was first proposed by Feistel [10]. Its Differential fault analysis, SPN, AES basic elements include a substitution transformation and a permutation transformation, which form the foundation of many modern block ciphers, such as AES etc. I. INTRODUCTION As a representative SPN structure, the security of AES During the last ten years a new class of attacks against against differential fault analysis has been investigated by cryptographic devices has become public [21]. These many researchers [1, 7-9, 11, 12]. There are two kinds of attacks exploit easily accessible information like power fault models concerning the security in general. One is consumption, running time, input-output behavior under the bit-oriented model. Several researchers have reported malfunctions, and can be mounted by anyone using low- that a single bit fault can be induced on the temporary cost equipment. These side-channel attacks amplify and result within AES [7, 12]. However, this kind of model evaluate leaked information with the help of statistical has its limitation because the operands of most computers methods, and are often much more powerful than are 'byte' or 'word', instead of 'bit'. In practice, it is not classical cryptanalysis. Examples show that a very small easy to induce a one-bit fault. So more important results amount of side-channel information is enough to has been drawn in the byte-oriented model since this fault completely break a cryptosystem [6, 14, 21]. While many model requires fewer faulty ciphertexts to mount the previously-known cryptanalytic attacks can be analyzed attack and makes more reasonable assumption. In the by studying algorithms, the vulnerabilities of side- byte-oriented model, P. Dusart et al. took advantage of a channel attacks result from electrical behavior of single-byte error occurring after the ShiftRows layer of transistors and circuits of an implementation. This the 9th round in AES-128. They used the particular form ultimately compromises cryptography, and shifts the top of the MixColumns and the SubBytes transformations to priority in cryptography from the further improvement of solve a list of equations [9]. The method requires about algorithms to the prevention of such attacks by reducing 40 faulty ciphertexts to recover the 128-bit secret key. variations in timing, power and radiation from the Under the same fault model, P. Gilles et al. induced errors hardware, and reduction of observability of system to the MixColumns transformations between the last but behavior after fault injection [2, 6, 17, 25]. Therefore, it one and two rounds [11]. This method only requires 2 extends theoretically the current mathematical models of faulty ciphertexts to recover 128-bit secret key. Later M. cryptography to the physical setting which takes into Amir et al. proposed a generalized method of DFA consideration side-channel attacks [4, 18, 20, 23]. against AES Their fault model covers all locations before the MixColumns transformation in the 9th round [1]. Corresponding author: Wei Li. They could recover 128-bit key of AES with 6 and 1500 Tel.: +86 1379 5438 126. faulty ciphertexts in two fault models. This generalized © 2011 ACADEMY PUBLISHER doi:10.4304/jcp.6.2.216-223 JOURNAL OF COMPUTERS, VOL. 6, NO. 2, FEBRUARY 2011 217 method uses a common and general assumption for error permutation transformation. In the substitution layer, locations and values. every current block is viewed as n m×n subblocks, each Although many researchers have investigated the of which is a bijective function mapping representative SPN cipher as above, the security of SPN {0,1}mm→ {0,1} . The permutation layer is originally a structure against differential fault analysis was only bit-wise permutation, but more generally an invertible published in [11]. In the byte-oriented fault model, a linear transformation [15, 16]. The permutation layer is single-byte fault can be induced to the diffusion layer in usually omitted in the last round. An example of a SPN the last but one round. By comparing the correct and structure is shown in Fig. 1. faulty ciphertexts, the attacker can retrieve part bytes or all bytes of the subkey in the last round. However, their practical attacking method still has its limitation because X the method can only recover one subkey, that is, the K 0 K0 K0 K 0 subkey in the last round. For some ciphers of SPN ⊕ 1 ⊕ 2 ⊕ 3 ⊕ n structure, the last subkey is not enough to recover all bits γ1 " in the secret key. For example, recovering the secret key of AES-256 cipher needs at least 2 subkeys. So the practical method in [11] is limited to recover only the last θ1 subkey of AES-256, not the whole secret key. As for the security of AES cipher, P. Gilles et al. σ 1 1 1 1 ⊕ K1 ⊕ K2 ⊕ K3 ⊕ Kn reported that their practical attack can be applied to AES " cipher with fewer faulty ciphertexts with less complexity [11]. However, we observe that this kind of practical " attacking technique only breaks the last subkey of AES- θ 128 since only the last round has no MixColumns R−2 transformation. As for AES-192 and AES-256, the last R−2 R−2 R−2 R−2 σ ⊕ K1 ⊕ K2 ⊕ K3 ⊕ Kn subkey is not enough to derive all bits in the secret key. R−1 R−1 R−1 R−1 A1 A2 A3 An Furthermore, M. Amir et al. pointed out that their method γ R−1 " is not applied to AES with 192-bit and 256-bit keys [1]. R−1 R−1 R−1 R−1 B1 B2 B Bn So the research in [1] and [11] is limited to recover AES- 2 128. In addition, P. Dusart et al. reported that their θR−1 method can be applied to AES with all key sizes and 10 KR−1 KR−1 KR−1 KR−1 ciphertexts to get four bytes of a subkey in the byte- σ ⊕ 1 ⊕ 2 ⊕ 3 ⊕ n R R R R oriented model [9]. In this case, to recover the secret key A A2 A A γ 1 3 n of AES-256 requires about 80 faulty ciphertexts. R " R R R BR Unfortunately, this method decreases the efficiency of B1 B2 B3 n fault injection and requires more faulty ciphertexts. σ R R R R ⊕ K1 ⊕ K2 ⊕ K3 ⊕ Kn We thus propose a new method to recover the secret key of SPN ciphers, with application to AES. It adopts Y the byte-oriented model, so the attacker can induce a single-byte error in the encryption. Compared with techniques available, our method can recover all subkeys Fig. 1. The Substitution-Permutation Network structure of SPN ciphers and be applied to SPN ciphers with more key sizes. As for AES-256, we only need 4 faulty In an SPN structure, the key schedule generates a total 01 R ciphertexts to recover the whole secret key. Our attacking of R+1 N-bit subkeys (,,,)KK" K by the original method on AES not only improves the efficiency of fault key K . injection, but also decreases the number of faulty 0 ciphertexts. The idea of this attack is also suitable for The plaintexts are XORed with the initial subkey K , AES-128, AES-192 and other SPN ciphers. and then the subkey K r are XORed with the output of This paper is organized as follows. Section 2 briefly the permutation layer in the r-th round with introduces the SPN structure. The next section describes 11≤ rR≤−. The last subkey K R is XORed with the the assumption of fault model, and proposes our method output of the substitution layer to form the ciphertext. of DFA on SPN structure. Then section 4 and 5 show our For the purpose of this paper, we adopt the following analysis on AES-256 and the experimental results. structure in the r-th round (11≤≤rR −). Finally section 5 concludes the paper. — The substitution layer n parallel m×n S-boxes: γ r rr γ rj()A = B j , II.
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