Revisiting the BGE Attack on a White-Box AES Implementation

White-box cryptography aims to protect the secret key of a cipher in an environment in which an adversary has full access to the implementation of the cipher and its execution environment. In 2002, Chow, Eisen, Johnson and van Oorschot proposed a white-box implementation of AES. In 2004, Billet, Gilbert and Ech-Chatbi presented an efficient attack (referred to as the BGE attack) on this implementation, extracting its embedded AES key with a work factor of $2^{30}$. In 2012, Tolhuizen presented an improvement of the most time-consuming phase of the BGE attack. This paper presents several improvements to the other phases of the BGE attack. The paper shows that the overall work factor of the BGE attack is reduced to $2^{22}$ when all improvements are implemented. In 2010, Karroumi presented a white-box AES implementation that is designed to withstand the BGE attack. This paper shows that the implementations of Karroumi and Chow \emph{et al.} are the same. As a result, Karroumi\u27s white-box AES implementation is vulnerable to the attack it was designed to resist

White-Box Cryptography: Analysis of White-Box AES Implementations (White-Box Cryptografie: Analyse van White-Box AES implementaties)

Cryptographic algorithms are designed to protect data or communication in the presence of an attacker. If these algorithms make use of a secret key, then their security relies on the secrecy of the key. Hence, the primary objective of an attacker typically is to extract the key. In a traditional black-box environment, the attacker has only access to the inputs and outputs of a cryptographic algorithm. However, due to the increasing demand to deploy strong cryptographic algorithms within software applications that are executed on untrusted open platforms owned and controlled by a possibly malicious party, the black-box environment becomes inadequate. Therefore, a new realistic white-box environment is introduced in which an attacker has complete access to a software implementation of a cryptographic algorithm and furthermore has full control over its execution environment. Real-world examples of a white-box environment can be found in digital content protection systems such as Digital Rights Management or Pay-TV systems, where key-instantiated cryptographic algorithms are implemented on e.g. a smartphone, tablet or set-top box. The extraction of the secret key would compromise the content protection.White-box cryptography aims to protect the confidentiality of the secret key of a cryptographic algorithm in a white-box environment. It is a technique to construct software implementations of a cryptographic algorithm that are sufficiently secure against a white-box attacker. In the academic literature, the focus has been mainly on the design of white-box implementations of block ciphers, an important subclass of symmetric-key cryptographic algorithms. In 2002, Chow, Eisen, Johnson and van Oorschot proposed the first published white-box implementation of the Advanced Encryption Standard (AES), one of the most prominent block ciphers at this time. However, two years later, Billet, Gilbert and Ech-Chatbi presented an efficient attack on this implementation, which motivated the design of three new white-box AES implementations offering more resistance against key extraction: the ones by Bringer, Chabanne and Dottax in 2006, by Xiao and Lai in 2009 and by Karroumi in 2010.This doctoral thesis covers the design and analysis of white-box implementations of block ciphers, where the main contributions address the analysis of white-box AES implementations. Starting from the initial improvement of Billet et al. s attack proposed by Tolhuizen in 2012, we present several additional improvements considerably reducing the overall work factor. Our improved version leads to some useful observations with respect to the design choices made in Chow et al. s white-box AES implementation. Further, this doctoral thesis describes the analysis of the three newly proposed white-box AES implementations mentioned above. First, we show how to efficiently extract equivalent keys out of Bringer et al. s white-box AES implementation; these equivalent keys yield functionally equivalent implementations. Second, we present a practical cryptanalysis of the white-box AES implementation proposed by Xiao and Lai. The cryptanalysis uses a modified variant of the linear equivalence algorithm presented by Biryukov, De Cannière, Braeken and Preneel as a building block. Additionally, we consider design generalizations of the Xiao-Lai white-box AES implementation and their impact on our cryptanalytic result. Third, we show that Karroumi s white-box AES implementation belongs to the class of white-box AES implementations specified by Chow et al. Consequently, Karroumi s implementation remains vulnerable to the attack it was designed to resist, i.e., Billet et al. s attack and our improved version of this attack.Based on the cryptanalytic results presented in this doctoral thesis and outlined above, it is shown that in early 2014 there does not exist a practical and secure white-box AES implementation published in the academic literature, even though AES is still considered to be a secure black-box block cipher. However, at the end of this thesis we discuss a new design principle proposed by Michiels and Gorissen that may lead to the construction of secure white-box AES implementations. All white-box AES implementations appeared in the academic literature so far are fixed-key; we present a new dynamic-key white-box technique that allows to update the cryptographic key in a more secure way than the known techniques.status: publishe

Cryptanalysis of a Perturbated White-box AES Implementation

In response to various cryptanalysis results on white-box cryptography, Bringer et al. presented a novel white-box strategy. They propose to extend the round computations of a block cipher with a set of random equations and perturbations, and complicate the analysis by implementing each such round as one system that is obfuscated with annihilating linear input and output encodings. The improved version presented by Bringer et al. implements the AEw/oS, which is an AES version with key-dependent S-boxes (the S-boxes are in fact the secret key). In this paper we present an algebraic analysis to recover equivalent keys from the implementation. We show how the perturbations and system of random equations can be distinguished from the implementation, and how the linear input and output encodings can be eliminated. The result is that we have decomposed the white-box implementation into a much more simple, functionally equivalent implementation and retrieved a set of keys that are equivalent to the original key. Our cryptanalysis has a worst time complexity of 2 17 and a negligible space complexity. © 2010 Springer-Verlag Berlin Heidelberg.status: publishe

Cryptanalysis of the Xiao - Lai White-Box AES Implementation

In the white-box attack context, i.e., the setting where an implementation of a cryptographic algorithm is executed on an untrusted platform, the adversary has full access to the implementation and its execution environment. In 2002, Chow et al. presented a white-box AES implementation which aims at preventing key-extraction in the white-box attack context. However, in 2004, Billet et al. presented an efficient practical attack on Chow et al.'s white-box AES implementation. In response, in 2009, Xiao and Lai proposed a new white-box AES implementation which is claimed to be resistant against Billet et al.'s attack. This paper presents a practical cryptanalysis of the white-box AES implementation proposed by Xiao et al. The linear equivalence algorithm presented by Biryukov et al. is used as a building block. The cryptanalysis efficiently extracts the AES key from Xiao et al.'s white-box AES implementation with a work factor of about 2 32 . © 2013 Springer-Verlag Berlin Heidelberg.status: publishe

Two Attacks on a White-Box AES Implementation

White-box cryptography aims to protect the secret key of a cipher in an environment in which an adversary has full access to the implementation of the cipher and its execution environment. In 2002, Chow, Eisen, Johnson and van Oorschot proposed a white-box implementation of AES. In 2004, Billet, Gilbert and Ech-Chatbi presented an efficient attack (referred to as the BGE attack) on this implementation, extracts extracting its embedded AES key with a work factor of 2 30 . In 2012, Tolhuizen presented an improvement of the most time-consuming phase of the BGE attack. The present paper includes three contributions. First we describe several improvements of the BGE attack. We show that the overall work factor of the BGE attack is reduced to 2 22 when all improvements are implemented. This paper also presents a new attack on the initial white-box implementation of Chow et al. This attack exploits collisions occurring on internal variables of the implementation and it achieves a work factor of 2 22 . Eventually, we address the white-box AES implementation presented by Karroumi in 2010 which aims to withstand the BGE attack. We show that the implementations of Karroumi and Chow et al. are the same, making them both vulnerable to the same attacks. © 2014 Springer-Verlag.status: publishe