On the practical security of white-box cryptography

Doctoral thesis (2020)

Cryptography studies how to secure communications and information. The security of a cryptosystem depends on the secrecy of the underlying key. White-box cryptography explores methods to hide a ... [more ▼]

Cryptography studies how to secure communications and information. The security of a cryptosystem depends on the secrecy of the underlying key. White-box cryptography explores methods to hide a cryptographic key into some software deployed in the real world. Classical cryptography only assumes that the adversary accesses the target cryptographic primitive in a black-box manner in which she can only observe or manipulate the input and output of the primitive, but cannot know or tamper with its internal details. The gray-box model further allows an adversary to exploit key- dependent sensitive information leaked from the execution of physical implementations. All sorts of side-channel attacks exploit some physical information leakage, such as the power consumption of the device. The white-box model considers the worst-case scenario in which the adversary has complete control over the software and its execution environment. The goal of white-box cryptography is to securely implement a cryptographic primitive against such a powerful adversary. Although the scientific community has proposed some candidate solutions to build white-box cryptography, all have proven ineffective. Consequently, this problem has remained open for almost two decades since the concept was introduced. The continuous growth in market demand and the emerging potential applications have driven the industry to deploy secretly-designed proprietary solutions. Al- though this paradigm of achieving security through obscurity contradicts the widely accepted Kerckhoffs' principle in cryptography, this is currently the only option for white-box cryptography. Security experts have reported how gray-box attacks could be used to extract keys from several publicly available white-box implementations. In a gray-box attack, the adversary adapts side-channel analysis techniques to the white-box context, i.e., to target computation traces made of noise-free run- time information instead of the noisy physical leakage. Gray-box attacks are generic since they do not require any a priori knowledge of the implementation and hence avoid costly reverse engineering. Some non-publicly scrutinized industrial white- box schemes in the market are believed to be under the threat of gray-box attacks. This thesis focuses on the analysis and improvement of gray-box attacks and the associated countermeasures for white-box cryptography. We first provide an in- depth analysis of why gray-box attacks are capable of breaking the classical white- box design which is based on table encodings. Next, we introduce a new gray-box at- tack named linear decoding analysis and show that linearly encoding sensitive information is insufficient to protect the cryptographic software. Afterward, we describe how to combine state-of-the-art countermeasures to resist gray-box attacks and comprehensively elaborate on the (in)effectiveness of these combined countermeasures in terms of computation complexity. Finally, we introduce a new attack technique that exploits the data-dependency of the targeted implementation to substantially lower the complexity of the existing gray-box attacks on white-box cryptography. In addition to the theoretical analyses and new attack techniques introduced in this thesis, we report some attack experiments against practical white-box implementations. In particular, we could break the winning implementations of two consecutive editions of the well-known WhibOx white-box cryptography competition. [less ▲]

How to reveal the secrets of an obscure white-box implementation

in Journal of Cryptographic Engineering (2019), 10(1), 49--66

White-box cryptography protects key extraction from software implementations of cryptographic primitives. It is widely deployed in DRM and mobile payment applications in which a malicious attacker might ... [more ▼]

White-box cryptography protects key extraction from software implementations of cryptographic primitives. It is widely deployed in DRM and mobile payment applications in which a malicious attacker might control the entire execution environment. So far, no provably secure white- box implementation of AES has been put forward, and all the published practical constructions are vulnerable to differential computation analysis (DCA) and differential fault analysis (DFA). As a consequence, the industry relies on home-made obscure white-box implementations based on secret designs. It is therefore of interest to investigate the achievable resistance of an AES implementation to thwart a white-box adversary in this paradigm. To this purpose, the ECRYPT CSA project has organized the WhibOx contest as the catch the flag challenge of CHES 2017. Researchers and engineers were invited to participate either as designers by submitting the source code of an AES-128 white-box implementation with a freely chosen key, or as breakers by trying to extract the hard-coded keys in the submitted challenges. The participants were not expected to disclose their identities or the underlying designing/attacking techniques. In the end, 94 submitted challenges were all broken and only 13 of them held more than 1 day. The strongest (in terms of surviving time) implementation, submitted by Biryukov and Udovenko, survived for 28 days (which is more than twice as much as the second strongest implementation), and it was broken by a single team, i.e., the authors of the present paper, with reverse engineering and algebraic analysis. In this paper, we give a detailed description of the different steps of our cryptanalysis. We then generalize it to an attack methodology to break further obscure white-box implementations. In particular, we formalize and generalize the linear decoding analysis that we use to extract the key from the encoded intermediate variables of the target challenge. [less ▲]

Analysis and Improvement of Differential Computation Attacks against Internally-Encoded White-Box Implementations

in IACR Transactions on Cryptographic Hardware and Embedded Systems (2019), 2019(2), 225-255

White-box cryptography is the last security barrier for a cryptographic software implementation deployed in an untrusted environment. The principle of internal encodings is a commonly used white-box ... [more ▼]

White-box cryptography is the last security barrier for a cryptographic software implementation deployed in an untrusted environment. The principle of internal encodings is a commonly used white-box technique to protect block cipher implementations. It consists in representing an implementation as a network of look-up tables which are then encoded using randomly generated bijections (the internal encodings). When this approach is implemented based on nibble (i.e. 4-bit wide) encodings, the protected implementation has been shown to be vulnerable to differential computation analysis (DCA). The latter is essentially an adaptation of differential power analysis techniques to computation traces consisting of runtime information, e.g., memory accesses, of the target software. In order to thwart DCA, it has then been suggested to use wider encodings, and in particular byte encodings, at least to protect the outer rounds of the block cipher which are the prime targets of DCA. In this work, we provide an in-depth analysis of when and why DCA works. We pinpoint the properties of the target variables and the encodings that make the attack (in)feasible. In particular, we show that DCA can break encodings wider than 4-bit, such as byte encodings. Additionally, we propose new DCA-like attacks inspired from side-channel analysis techniques. Specifically, we describe a collision attack particularly effective against the internal encoding countermeasure. We also investigate mutual information analysis (MIA) which naturally applies in this context. Compared to the original DCA, these attacks are also passive and they require very limited knowledge of the attacked implementation, but they achieve significant improvements in terms of trace complexity. All the analyses of our work are experimentally backed up with various attack simulation results. We also verified the practicability of our analyses and attack techniques against a publicly available white-box AES implementation protected with byte encodings –which DCA has failed to break before– and against a “masked” white-box AES implementation –which intends to resist DCA. [less ▲]