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White-Box Implementation of the Identity-Based Signature Scheme in the IEEE P1363 Standard for Public Key Cryptography

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White-Box Implementation of the Identity-Based Signature Scheme in the IEEE P1363 Standard for Public Key Cryptography IEICE TRANS. INF. & SYST., VOL.E103–D, NO.2 FEBRUARY 2020 188 INVITED PAPER Special Section on Security, Privacy, Anonymity and Trust in Cyberspace Computing and Communications White-Box Implementation of the Identity-Based Signature Scheme in the IEEE P1363 Standard for Public Key Cryptography Yudi ZHANG†,††, Debiao HE†,††a), Xinyi HUANG†††,††††, Ding WANG††,†††††, Kim-Kwang Raymond CHOO††††††, Nonmembers, and Jing WANG†,††, Student Member SUMMARY Unlike black-box cryptography, an adversary in a white- box security model has full access to the implementation of the crypto- graphic algorithm. Thus, white-box implementation of cryptographic algo- rithms is more practical. Nevertheless, in recent years, there is no white- box implementation for public key cryptography. In this paper, we propose Fig. 1 A typical DRM architecture the first white-box implementation of the identity-based signature scheme in the IEEE P1363 standard. Our main idea is to hide the private key to multiple lookup tables, so that the private key cannot be leaked during the algorithm executed in the untrusted environment. We prove its security in both black-box and white-box models. We also evaluate the performance gram. However, the adversary does not have the permis- of our white-box implementations, in order to demonstrate utility for real- sion to access the internal process of the program’s execu- world applications. tion. In practice, an adversary can also observe and mod- key words: white-box implementation, white-box security, IEEE P1363, ify the algorithm’s implementation to obtain the internal de- identity-based signature, key extraction tails, such as the secret key. Many side-channel attacks have been proposed recently, most of them can be mounted on 1. Introduction the existing cryptographic systems, such as timing, power, and fault analysis attacks. For example, the digital rights White-box cryptography was first introduced by Chow et management (DRM) is commonly used to restrict the use of al. [1], [2] in 2002, and is designed to prevent software proprietary hardware and copyrighted works. In the exam- implementation of cryptographic algorithm from being at- ple shown in Fig. 1, a broadcasting company wishes to dis- tacked in untrusted envrionments. Specifically, the key pur- tribute their digital content (e.g., music and movies) on the pose of white-box cryptography is to ensure the confiden- Internet, and set different permissions to the users such that tiality of secret keys. Since the first white-box implementa- only paying users can access the purchased content. How- tions of DES and AES algorithms [1], [2], a number of other ever, these users should not be able to copy or re-distribute white-box implementations have been proposed in the liter- the content. Therefore, the provider should encrypt the con- ature [3], [4]. tent m first, i.e., computes c = Enck(m), then distributes the In the trusted environment, an adversary knows the al- entrypted content c on the public network. If the user has gorithm of the cryptographic system. The adversary can also the license to access the content, then the Rights Expression require a number of inputs and obtain outputs from the pro- Manager can parse the user’s authentication and decrypt the encrypted content, i.e., the corresponding decryption pro- Manuscript received March 3, 2019. gram D computes m = Deck(c) to obtain the original con- Manuscript revised June 19, 2019. tent. However, iTunes DRM has been reportedly cracked Manuscript publicized September 27, 2019. † by Johansen [5], where the vulnerability can be exploited The authors are with Key Laboratory of Aerospace Infor- mation Security and Trusted Computing, Ministry of Education, to re-distribute the content without authentication. Similar School of Cyber Science and Engineering, Wuhan University, vulnerabilities in iOS DRM applications have been revealed Wuhan 430072, China. by D’Orazio and Choo [6], which can be exploited to gain †† The authors are with State Key Laboratory of Cryptology, access to copyrighted materials for free. P.O. Box 5159, Beijing 100878, China. ff ††† As more DRM services are o ered via mobile de- The author is with the College of Mathematics and Informat- vices / applications (apps), it is vital to ensure the secu- ics, Fujian Normal University, Fuzhou 350117, China. / ††††The author is with the Fujian Provincial Key Laboratory of rity of DRM and other services apps, for example the use Network Security and Cryptology, Fuzhou 350117, China. of cryptographic tools such as encryption and digital signa- †††††The author is with School of Electronics Engineering and ture schemes. The latter is indispensable in the Internet es- Computer Science, Peking University, Beijing 100871, China. pecially in e-commerce, due to its capability to demonstrate †††††† The author is with Department of Information Systems and the validity of user’s message and identity. Formally, a valid Cyber Security and the Department of Electrical and Computer En- digital signature ensures that the message was generated by gineering, The University of Texas at San Antonio, San Antonio, / TX 78249, USA. a known signer, the signer cannot deny his her signature, a) E-mail: [email protected] and that the integrity of the message has not been compro- DOI: 10.1587/transinf.2019INP0004 mised. To avoid the limitations inherent in public key-based Copyright c 2020 The Institute of Electronics, Information and Communication Engineers ZHANG et al.: WHITE-BOX IMPLEMENTATION OF THE IDENTITY-BASED SIGNATURE SCHEME IN THE IEEE P1363 STANDARD 189 2. Related Work White-box cryptography (WBC) is designed to protect soft- ware implementations of cryptographic algorithms when the software is running on untrusted environment, in the sense that the adversary has full access to the implemen- tation [1], [2].Chowet al. [1], [2] proposed the first white-box implementation for both DES and AES algo- rithms, and the authors also introduced the White-Box At- tack Context (WBAC). In WBAC, the adversary seeks to extract the secret keys from the implementation. In re- cent years, many other white-box implementations have also been put forward, such as white-box implementations of DES and AES [3], [4], many of these schemes have been shown to be vulnerable to practical key extraction or table- Fig. 2 A use case for white-box implementation in wireless environment decomposition attacks [16]–[18]. For example, using lin- ear algebra, Lepoint et al. [18] demonstrated how Lepoint’s construction can be broken. Biryukov et al. [19] also broke digital signature schemes, such as those of [7]–[9], Shamir Chow et al.’s construction in 2014. introduced the first identity-based cryptography [10]. Since Billet et al. [16] proposed an effective cryptanalysis for the seminal work of Shamir, many other identity-based sig- white-box implementations of AES algorithm in 2004. They nature (IBS) schemes, such as those of [11]–[14], have been used algebraic cryptanalysis to analyze specific lookup ta- proposed in the literature. bles, and removed the non-linear parts of the internal im- While identity-based digital signature is a topic that has plementation. In a later work, Michiels et al. [20] proposed been extensively studied, there is not any known white-box an improved cryptanalysis, which can be used to analyze a implementation of identity-based signature scheme. Thus, generic class of white-box implementations. this is the focus and contribution of the work in this paper. Biryukov et al. [19] also showed that the white-box im- Specifically, in our study, we focus on the white-box imple- plementations of AES and DES [1], [2] can be identified as mentation of identity-based signature scheme in the IEEE a 3-layer ASA (affine-substitution-affine) structure, and they P1363 standard for public key cryptography [15].Asfar proposed a more secure structure (i.e., a 5-layer ASASA as we know, this is the first white-box implementation of construction). Since the work of Biryukov et al. [19], other identity-based signature scheme (in the IEEE P1363 stan- researchers [21], [22] have studied the decomposition of se- dard). Our method is lightweight, and meets the white-box cret nonlinear and linear layers. Theoretically, the more lay- security requirement. As shown in Fig. 2, our method can ers that are employed, the more secure the construction is. be implemented in an untrusted wireless environment, in- However, Biryukov et al. [23] also showed that even a 9- cluding on mobile devices such as Android or iOS device. layer construction SASASASAS is vulnerable. Specifically, the Sign algorithm is implemented on some Delerabl et al. [24] proposed a notion of incompress- user devices in the white-box model. Therefore, the mali- ibility: an adversary has full access to the white-box imple- cious applications or hackers obtaining user’s private key is mentation, but generate a program with the same function impossible. Moreover, even if the device is lost, no one can and dramatically small size is impossible. Such a notion get the user’s private key. is also referred to as weak white-box [19] or space hard- In Sect. 2, we introduce related white-box cryptogra- ness [25] in the literature. In this notion, the adversary can- phy literature, prior to presenting the notations, the identity- not extract the key from the white-box implementation of based signature scheme in the IEEE P1363 standard, math- the cryptographic algorithm, if the implementation is large ematical assumptions and the definitions of white-box se- and incompressible. curity in Sect. 3. In Sect. 4, we propose our white-box im- More recently in 2016, Bellare et al. [26] utilized a plementation of the identity-based signature scheme in the large encryption key to protect the key, which is called the IEEE P1363 standard, and give the description of the de- bounded-retrieval model (BRM), and Fouque et al.
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