White-box Cryptography Research Articles

Quantum-Resistance Meets White-Box Cryptography: How to Implement Hash-Based Signatures against White-Box Attackers?

The adversary model of white-box cryptography includes an extreme case where the adversary, sitting at the endpoint, has full access to a cryptographic scheme. Motivating by the fact that most existing white-box implementations focus on symmetric encryption, we present implementations for hash-based signatures so that the security against white-box attackers (who have read-only access to data with a size bounded by a space-hardness parameter M) depends on the availability of a white-box secure cipher (in addition to a general one-way function). We also introduce parameters and key-generation complexity results for white-box secure instantiation of stateless hash-based signature scheme SPHINCS+, one of the NIST selections for quantum-resistant digital signature algorithms, and its older version SPHINCS. We also present a hash tree-based solution for one-time passwords secure in a white-box attacker context. We implement the proposed solutions and share our performance results.

LWARX: Lightweight ARX white-box cipher for satellite communications

Satellite communication links are vulnerable to attacks due to the lack of necessary security protection and can be considered as a white-box environment. In a white-box environment, cryptanalysts can access the intermediate processes of the algorithm and even manipulate or change the operating environment. Cryptanalysts can obtain keys or tamper with important data in many ways, which makes data communication unsecured. To solve the problem, a lightweight white-box cipher over Addition/Rotation/XOR (ARX) structure (LWARX) is proposed, which has 48 rounds of iterations through an unbalanced Feistel structure. On this basis, some of its linear operations are represented as lookup tables, and a secure external coding method is combined to complete the white-box implementation. The design and white-box implementation of the algorithm has resulted in a lighter and more rational structure, and still provides sufficient obfuscation of the data even when the S-box is discarded. The test results show that the average encryption speed is 37.53 Kbps, and average encryption speed after white-box implementation is 30.05 Kbps. And it can resist various attacks. The security of the algorithm against common attack methods such as differential analysis, linear analysis, code lifting attacks and BGE attacks is given in the paper with security analysis and specific values. This scheme balances computing efficiency and security, takes up little space, can be applied to scenarios with limited hardware and software resources, and broadens the application area of white-box cryptography.

UpWB: An Uncoupled Architecture Design for White-box Cryptography Using Vectorized Montgomery Multiplication

UpWB: An Uncoupled Architecture Design for White-box Cryptography Using Vectorized Montgomery Multiplication

An approach for designing fast public key encryption systems using white-box cryptography techniques

An approach for designing fast public key encryption systems using white-box cryptography techniques

화이트 박스 블록 암호에 대한 최신 암호분석 기술 동향 연구

Black box cryptography is a cryptographic scheme based on a hardware encryption device, operating under the assumption that the device and the user can be trusted. However, with the increasing use of cryptographic algorithms on unreliable open platforms, the threats to black box cryptography systems have become even more significant. As a consequence, white box cryptography have been proposed to securely operate cryptographic algorithms on open platforms by hiding encryption keys during the encryption process, making it difficult for attackers to extract the keys. However, unlike traditional cryptography, white box-based encryption lacks established specifications, making it challenging to verify its structural security. To promote the safer utilization of white box cryptography, CHES organizes The WhibOx Contest periodically, which conducts safety analyses of various white box cryptographic techniques. Among these, the Differential Computation Analysis (DCA) attack proposed by Bos in 2016 is widely utilized in safety analyses and represents a powerful attack technique against robust white box block ciphers. Therefore, this paper analyzes the research trends in white box block ciphers and provides a summary of DCA attacks and relevant countermeasures, adhering to the format of a research paper..

Cryptanalysis Of A Type Of White-Box Implementations Of The SM4 Block Cipher

Abstract The SM4 block cipher is a Chinese national standard and an ISO international standard. Since white-box cryptography has many real-life applications nowadays, a few white-box implementations of SM4 has been proposed, among which a type of constructions is dominated, which uses a linear or affine diagonal block encoding to protect the original three 32-bit branches entering a round function and uses its inverse as the input encoding to the S-box layer. In this paper, we analyse the security of this type of constructions against Lepoint et al.’s collision-based attack method. Our experiment under a small fraction of (encodings, round key) combinations shows that the rank of the concerned linear system is much less than the number of the involved unknowns, meaning these white-box SM4 implementations should resist Lepoint et al.’s method, but we leave it as an open problem whether there are such encodings that the rank of the corresponding linear system is slightly less than the number of the involved unknowns, in which scenario Lepoint et al.’s method may be used to recover a round key for the case with linear encodings and to remove most white-box operations until mainly some Boolean masks for the case with affine encodings.

On Provable White-Box Security in the Strong Incompressibility Model

Incompressibility is a popular security notion for white-box cryptography and captures that a large encryption program cannot be compressed without losing functionality. Fouque, Karpman, Kirchner and Minaud (FKKM) defined strong incompressibility, where a compressed program should not even help to distinguish encryptions of two messages of equal length. Equivalently, the notion can be phrased as indistinguishability under chosen-plaintext attacks and key-leakage (LK-IND-CPA), where the leakage rate is high.In this paper, we show that LK-IND-CPA security with superlogarithmic-length leakage, and thus strong incompressibility, cannot be proven under standard (i.e. single-stage) assumptions, if the encryption scheme is key-fixing, i.e. a polynomial number of message-ciphertext pairs uniquely determine the key with high probability. Our impossibility result refutes a claim by FKKM that their big-key generation mechanism achieves strong incompressibility when combined with any PRG or any conventional encryption scheme, since the claim is not true for encryption schemes which are key-fixing (or for PRGs which are injective). In particular, we prove that the cipher block chaining (CBC) block cipher mode is key-fixing when modelling the cipher as a truly random permutation for each key. Subsequent to and inspired by our work, FKKM prove that their original big-key generation mechanism can be combined with a random oracle into an LK-IND-CPA-secure encryption scheme, circumventing the impossibility result by the use of an idealised model.Along the way, our work also helps clarifying the relations between incompressible white-box cryptography, big-key symmetric encryption, and general leakage resilient cryptography, and their limitations.

LPN-based Attacks in the White-box Setting

In white-box cryptography, early protection techniques have fallen to the automated Differential Computation Analysis attack (DCA), leading to new countermeasures and attacks. A standard side-channel countermeasure, Ishai-Sahai-Wagner’s masking scheme (ISW, CRYPTO 2003) prevents Differential Computation Analysis but was shown to be vulnerable in the white-box context to the Linear Decoding Analysis attack (LDA). However, recent quadratic and cubic masking schemes by Biryukov-Udovenko (ASIACRYPT 2018) and Seker-Eisenbarth-Liskiewicz (CHES 2021) prevent LDA and force to use its higher-degree generalizations with much higher complexity.In this work, we study the relationship between the security of these and related schemes to the Learning Parity with Noise (LPN) problem and propose a new automated attack by applying an LPN-solving algorithm to white-box implementations. The attack effectively exploits strong linear approximations of the masking scheme and thus can be seen as a combination of the DCA and LDA techniques. Different from previous attacks, the complexity of this algorithm depends on the approximation error, henceforth allowing new practical attacks on masking schemes which previously resisted automated analysis. We demonstrate it theoretically and experimentally, exposing multiple cases where the LPN-based method significantly outperforms LDA and DCA methods, including their higher-order variants.This work applies the LPN problem beyond its usual post-quantum cryptography boundary, strengthening its interest for the cryptographic community, while expanding the range of automated attacks by presenting a new direction for breaking masking schemes in the white-box model.

Even-Mansour Space-hard Cipher: White-box Cryptography Cipher Meets Physically Unclonable Function

Even-Mansour Space-hard Cipher: White-box Cryptography Cipher Meets Physically Unclonable Function

AES Based White Box Cryptography in Digital Signature Verification

According to the standard paradigm, white box cryptographic primitives are used to block black box attacks and protect sensitive information. This is performed to safeguard the protected information and keys against black box assaults. An adversary in such a setting is aware of the method and can analyze many system inputs and outputs, but is blind to the specifics of how a critical instantiation primitive is implemented. This is the focus of white-box solutions, which are designed to withstand attacks that come from the execution environment. This is significant because an attacker may obtain unrestricted access to the program's execution in this environment. The purpose of this article is to assess the efficiency of white-box implementations in terms of security. Our contribution is twofold: first, we explore the practical implementations of white-box approaches, and second, we analyze the theoretical foundations upon which these implementations are built. First, a research proposal is crafted that details white-box applications of DES and AES encryption algorithms. To begin, this preparation is necessary. The research effort planned for this project also includes cryptanalysis of these techniques. Once the general cryptanalysis results have been examined, the white-box design approaches will be covered. We have decided to launch an investigation into creating a theoretical model for white box, since no prior formal definitions have been offered, and suggested implementations have not been accompanied by any assurance of security. This is due to the fact that no formal definition of "white box" has ever been provided. In this way lies the explanation for why this is the situation. We define WBC to encompass the security requirements of WBC specified over a white box cryptography technology and a security concept by studying formal models of obfuscation and shown security. This definition is the product of extensive investigation. This state-of-the-art theoretical model provides a setting in which to investigate the security of white-box implementations, leading to a wide range of positive and negative conclusions. As a result, this paper includes the results of a Digital Signature Algorithm (DSA) study which may be put to use in the real world with signature verification. Possible future applications of White Box Cryptography (WBC) research findings are discussed in light of these purposes and areas of investigation.

Hybrid Code Lifting on Space-Hard Block Ciphers

There is a high demand for whitebox cryptography from the practical use of encryption in untrusted environments. It has been actively discussed for two decades since Chow et al. presented the whitebox implementation of DES and AES. The goal is to resist the key extraction from the encryption program and mitigate the code lifting of the program. At CCS2015, Bogdanov and Isobe proposed space-hard block ciphers as a dedicated design of whitebox block ciphers. It ensures that the key extraction is as difficult as the key recovery in the standard blackbox model. Moreover, to mitigate code lifting, they introduce space hardness, a kind of leakage-resilient security with the incompressibility of a huge program. For space-hard ciphers, code lifting (a partial leakage of the entire program) is useless to copy the functionality.In this paper, we consider a new attack model of space-hard block ciphers called hybrid code lifting. Space-hard block ciphers are intended to ensure security under a size-bounded leakage. However, they do not consider attackers (in the standard blackbox model) receiving the leakage by code lifting. If such attackers can recover the encryption program of a space-hard block cipher, such a cipher does not always satisfy the intention. We analyze Yoroi proposed in TCHES 2021. We introduce the canonical representation of Yoroi. Using the representation enables the recovery of the programs of Yoroi-16 and Yoroi-32 with 233 and 265.6 complexities, respectively, in spite of slight leakage. The canonical representation causes another attack against Yoroi. It breaks an authors’ security claim about the “longevity”. We additionally analyzed SPNbox proposed in Asiacrypt 2016. As a result, considering security on the hybrid code lifting, the original number of rounds is insufficient to achieve 128-bit security under quarter-size leakage.

Honey Encryption Applied to Schnorr Signature Scheme

The security of any cryptosystem mostly depends on the reliability of the protection of secret keys used in it. In particular, key generation procedure must give a variety of keys so that they cannot be picked up by a brute-force attack. Honey encryption is used as an additional barrier of cryptosystems' keys protection to slow down a brute-force attack. As in the case of " white box cryptography'', different honey encryption schemes are considered depending on what the additional protection is aimed at. The need to additionally protect secret keys arises in remote access systems, when it is necessary to provide access to information to authorized users.The idea of encryption, which would provide adequate additional protection, is to build a system so that the attacker will not be able to recover the original text, even after searching through all possible options for passwords or keys. Based on the concept of lure systems, this system outputs messages that are difficult to distinguish from the true ones. Such messages are called honey, which, like the sweet substance, but in computer security terminology, " drag '' the opponent into a dead end.This article constructs schemes for additional key protection of the Schnorr Signature Scheme, describes the pseudocodes of the corresponding algorithms, analyzes the complexity of a brute-force attack.This scheme requires additional protection against the a secret key because storing it in the open is unreliable. With the proposed encryption algorythm, we can "hide'' a into a sequence of integers, and extract it back with the proposed decryption algorythm. If the sequence is entered by an attacker and does not contain a masked number a , decryption algorythm will return the result of multiplying the last number by the inverse q to the first prime number, if any, in the set, or the penultimate number in the set. Therefore, when trying to artificially pick up a secret key by a brute-force attack, the attacker will get a number similar to a but which he will not be able to use when trying to forge Alice's signature.

Cryptanalysis of a white‐box SM4 implementation based on collision attack

White-box cryptography is to primarily protect the key of a cipher from being extracted in a white-box scenario, where an adversary has full access to the execution environment of software implementation. Since the introduction of white-box cryptography, a number of white-box implementations of the Chinese SM4 block cipher standard have been proposed, and all of them have been attacked based on Billet et al.’s attack. In this study, we show that collision-based attack can work more efficiently on Shi et al.’s white-box SM4 implementation than the previously published attacks, by devising an attack with a time complexity of 2 23 , significantly reducing the previously known time complexity of 2 49 to a very practical level. Our attack can also be similarly applied to some other white-box SM4 implementations.

Structural Attack (and Repair) of Diffused-Input-Blocked-Output White-Box Cryptography

In some practical enciphering frameworks, operational constraints may require that a secret key be embedded into the cryptographic algorithm. Such implementations are referred to as White-Box Cryptography (WBC). One technique consists of the algorithm’s tabulation specialized for its key, followed by obfuscating the resulting tables. The obfuscation consists of the application of invertible diffusion and confusion layers at the interface between tables so that the analysis of input/output does not provide exploitable information about the concealed key material.Several such protections have been proposed in the past and already cryptanalyzed thanks to a complete WBC scheme analysis. In this article, we study a particular pattern for local protection (which can be leveraged for robust WBC); we formalize it as DIBO (for Diffused-Input-Blocked-Output). This notion has been explored (albeit without having been nicknamed DIBO) in previous works. However, we notice that guidelines to adequately select the invertible diffusion ∅and the blocked bijections B were missing. Therefore, all choices for ∅ and B were assumed as suitable. Actually, we show that most configurations can be attacked, and we even give mathematical proof for the attack. The cryptanalysis tool is the number of zeros in a Walsh-Hadamard spectrum. This “spectral distinguisher” improves on top of the previously known one (Sasdrich, Moradi, Güneysu, at FSE 2016). However, we show that such an attack does not work always (even if it works most of the time).Therefore, on the defense side, we give a straightforward rationale for the WBC implementations to be secure against such spectral attacks: the random diffusion part ∅ shall be selected such that the rank of each restriction to bytes is full. In AES’s case, this seldom happens if ∅ is selected at random as a linear bijection of F322. Thus, specific care shall be taken. Notice that the entropy of the resulting ∅ (suitable for WBC against spectral attacks) is still sufficient to design acceptable WBC schemes.

Yoroi: Updatable Whitebox Cryptography

Whitebox cryptography aims to provide security in the whitebox setting where the adversary has unlimited access to the implementation and its environment. In order to ensure security in the whitebox setting, it should prevent key extraction attacks and code-lifting attacks, in which the adversary steals the original cryptographic implementation instead of the key, and utilizes it as a big key. Although recent published ciphers such as SPACE, SPNbox, and Whiteblock successfully achieve security against the key extraction attacks, they only provide mitigation of codelifting attack by the so-called space hardness and incompressibility properties of the underlying tables as the space-hard/incompressible table might be eventually stolen by continuous leakage. The complete prevention of such attacks may need to periodically update the secret key. However, that entails high costs and might introduce an additional vulnerability into the system due to the necessity for the reencryption of all data by the updated key. In this paper, we introduce a new property, denominated longevity, for whitebox cryptography. This property enhances security against code-lifting attacks with continuous leakage by updating incompressible tables instead of the secret key. We propose a family of new whitebox-secure block ciphers Yoroi that has the longevity property in addition to the space hardness. By updating its implementation periodically, Yoroi provides constant security against code-lifting attacks without key updating. Moreover, the performance of Yoroi is competitive with existing ciphers implementations in the blackbox and whitebox context.

A White-Box Masking Scheme Resisting Computational and Algebraic Attacks

White-box cryptography attempts to protect cryptographic secrets in pure software implementations. Due to their high utility, white-box cryptosystems (WBC) are deployed by the industry even though the security of these constructions is not well defined. A major breakthrough in generic cryptanalysis of WBC was Differential Computation Analysis (DCA), which requires minimal knowledge of the underlying white-box protection and also thwarts many obfuscation methods. To avert DCA, classic masking countermeasures originally intended to protect against highly related side-channel attacks have been proposed for use in WBC. However, due to the controlled environment of WBCs, new algebraic attacks against classic masking schemes have quickly been found. These algebraic DCA attacks break all classic masking countermeasures efficiently, as they are independent of the masking order.In this work, we propose a novel generic masking scheme that can resist both DCA and algebraic DCA attacks. The proposed scheme extends the seminal work by Ishai et al. which is probing secure and thus resists DCA, to also resist algebraic attacks. To prove the security of our scheme, we demonstrate the connection between two main security notions in white-box cryptography: probing security and prediction security. Resistance of our masking scheme to DCA is proven for an arbitrary order of protection, using the well-known strong non-interference notion by Barthe et al. Our masking scheme also resists algebraic attacks, which we show concretely for first and second-order algebraic protection. Moreover, we present an extensive performance analysis and quantify the overhead of our scheme, for a proof-of-concept protection of an AES implementation.

White-Box Implementation of ECDSA Based on the Cloud Plus Side Mode

White-box attack context assumes that the running environments of algorithms are visible and modifiable. Algorithms that can resist the white-box attack context are called white-box cryptography. The elliptic curve digital signature algorithm (ECDSA) is one of the most widely used digital signature algorithms which can provide integrity, authenticity, and nonrepudiation. Since the private key in the classical ECDSA is plaintext, it is easy for attackers to obtain the private key. To increase the security of the private key under the white-box attack context, this article presents an algorithm for the white-box implementation of ECDSA. It uses the lookup table technology and the “cloud plus side” mode to protect the private key. The residue number system (RNS) theory is used to reduce the size of storage. Moreover, the article analyzes the security of the proposed algorithm against an exhaustive search attack, a random number attack, a code lifting attack, and so on. The efficiency of the proposed scheme is compared with that of the classical ECDSA through experiments.

Defeating State-of-the-Art White-Box Countermeasures with Advanced Gray-Box Attacks

The goal of white-box cryptography is to protect secret keys embedded in a cryptographic software deployed in an untrusted environment. In this article, we revisit state-of-the-art countermeasures employed in white-box cryptography, and we discuss possible ways to combine them. Then we analyze the different gray-box attack paths and study their performances in terms of required traces and computation time. Afterward, we propose a new paradigm for the gray-box attack against white-box cryptography, which exploits the data-dependency of the target implementation. We demonstrate that our approach provides substantial complexity improvements over the existing attacks. Finally, we showcase this new technique by breaking the three winning AES-128 white-box implementations from WhibOx 2019 white-box cryptography competition.

A Secure Shuffling Mechanism for White-Box Attack-Resistant Unmanned Vehicles

Unmanned Vehicles (UVs) have been being utilized for various applications, such as surveillance, search/rescue, and monitoring. The information they transmit is critical for decision-making. However, UVs are vulnerable to white-box attacks due to improvements in reverse engineering techniques and the openness of their software. Therefore, attackers with sufficient knowledge of a target UV can steal secret information stored in the UV by exploiting its vulnerabilities. Recently, several white-box cryptography techniques have been introduced to protect secret keys from being extracted by converting them into large look-up tables. However, none of them provide approaches to securely update the look-up tables. Thus, once a remote attacker succeeds in extracting the static look-up table from a UV, he/she can use it to decrypt past/future communications or to send false information to the control station by impersonating the UV. In this paper, we propose a look-up table shuffling mechanism that supports white-box cryptography with dynamics. The mechanism makes it hard for attackers to determine the positions of the table entries, and thus to decrypt/encrypt ciphertexts/plaintexts. To show the practicality of the block cipher with our mechanism, we implemented it on a board equipped with a GPU and show its GPU-accelerated performance.

On the Security Goals of White-Box Cryptography

We discuss existing and new security notions for white-box cryptography and comment on their suitability for Digital Rights Management and Mobile Payment Applications, the two prevalent use-cases of white-box cryptography. In particular, we put forward indistinguishability for white-box cryptography with hardware-binding (IND-WHW) as a new security notion that we deem central. We also discuss the security property of application-binding and explain the issues faced when defining it as a formal security notion. Based on our proposed notion for hardware-binding, we describe a possible white-box competition setup which assesses white-box implementations w.r.t. hardware-binding. Our proposed competition setup allows us to capture hardware-binding in a practically meaningful way.While some symmetric encryption schemes have been proven to admit plain white-box implementations, we show that not all secure symmetric encryption schemes are white-boxeable in the plain white-box attack scenario, i.e., without hardware-binding. Thus, even strong assumptions such as indistinguishability obfuscation cannot be used to provide secure white-box implementations for arbitrary ciphers. Perhaps surprisingly, our impossibility result does not carry over to the hardware-bound scenario. In particular, Alpirez Bock, Brzuska, Fischlin, Janson and Michiels (ePrint 2019/1014) proved a rather general feasibility result in the hardware-bound model. Equally important, the apparent theoretical distinction between the plain white-box model and the hardware-bound white-box model also translates into practically reduced attack capabilities as we explain in this paper.