This work proposes a new white-box attack technique called filtering, which can be combined with any other trace-based attack method. The idea is to filter the traces based on the value of an intermediate variable in the implementation, aiming to fix a share of a sensitive value and degrade the security of an involved masking scheme. Coupled with LDA (filtered LDA, FLDA), it leads to an attack defeating the state-of-the-art SEL masking scheme (CHES 2021) of arbitrary degree and number of...

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...

Fully Homomorphic Encryption (FHE) is a powerful Privacy-Enhancing Technology (PET) that enables computations on encrypted data without having access to the secret key. While FHE holds immense potential for enhancing data privacy and security, creating its practical applications is associated with many difficulties. A significant barrier is the absence of easy-to-use, standardized components that developers can utilize as foundational building blocks. Addressing this gap requires...

Software obfuscation is a powerful tool to protect the intellectual property or secret keys inside programs. Strong software obfuscation is crucial in the context of untrusted execution environments (e.g., subject to malware infection) or to face potentially malicious users trying to reverse-engineer a sensitive program. Unfortunately, the state-of-the-art of pure software-based obfuscation (including white-box cryptography) is either insecure or infeasible in practice. This work...

Algorithm hardness can be described by 5 categories: hardness in computation, in sequential computation, in memory, in energy consumption (or bandwidth), in code size. Similarly, hardness can be a concern for solving or for verifying, depending on the context, and can depend on a secret trapdoor or be universally hard. Two main lines of research investigated such problems: cryptographic puzzles, that gained popularity thanks to blockchain consensus systems (where solving must be moderately...

Protecting secret keys from malicious observers in untrusted environments is a critical security issue. White-box cryptography suggests software protection by hiding the key in the white-box setting. One method for hiding the key in the cipher code is through encoding methods. Unfortunately, encoding methods may be vulnerable to algebraic attacks and side-channel analysis. Another technique to hide the key is (M,Z)-space hardness approach that conceals the key into a large lookup table...

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...

Indistinguishability obfuscation (IO) is at the frontier of cryptography research for several years. LV16/Lin17 obfuscation schemes are famous progresses towards simplifying obfuscation mechanism. In fact, these two schemes only constructed two compact functional encryption (CFE) algorithms, while other things were taken to AJ15 IO frame or BV15 IO frame. That is, CFE algorithms are inserted into AJ15 IO frame or BV15 IO frame to form a complete IO scheme. The basic structure of two CFE...

One of the main security challenges white-box cryptography needs to address is side-channel security. To this end, designers aim to eliminate the dependence between variables and sensitive data. Classical countermeasures to do so are masking schemes. Nevertheless, most masking schemes are not designed to thwart the other main security threat : fault attacks. Thus, we aimed to build a masking scheme that could combine resistance to both of these types of attacks. In this paper, we...

Incompressibility is one of the most fundamental security goals in white-box cryptography. Given recent advances in the design of efficient and incompressible block ciphers such as SPACE, SPNbox and WhiteBlock, we demonstrate the feasibility of reducing incompressible AEAD modes to incompressible block ciphers. We first observe that several existing AEAD modes of operation, including CCM, GCM(-SIV), and OCB, would be all insecure against white-box adversaries even when used with an...

One of the main challenges cryptography needs to deal with is balancing the performances of a cryptographic primitive with its security. That is why in 2015, the National Institute of Standards and Technologies (NIST) has begun a standardization process to solicit the creation of new lightweight cryptographic algorithms. We then wondered which of this standardization finalists would suit the best to a white-box implementation. To this end, we studied different algorithms structures on...

This paper deals with white-box implementations of the Elliptic Curve Digital Signature Algorithm (ECDSA): First, we consider attack paths to break such implementations. In particular, we provide a systematic overview of various fault attacks, to which ECDSA white-box implementations are especially susceptible. Then, we propose different mathematical countermeasures, mainly based on masking/blinding of sensitive variables, in order to prevent or at least make such attacks more difficult. We...

In 2002, Chow et al. initiated the formal study of white-box cryptography and introduced the CEJO framework. Since then, various white-box designs based on their framework have been proposed, all of them broken. Ranea and Preneel proposed a different method in 2020, called self-equivalence encodings and analyzed its security for AES. In this paper, we apply this method to generate the first academic white-box Speck implementations using self-equivalence encodings. Although we focus on Speck...

Since the first white-box implementation of AES published twenty years ago, no significant progress has been made in the design of secure implementations against an attacker with full control of the device. Designing white-box implementations of existing block ciphers is a challenging problem, as all proposals have been broken. Only two white-box design strategies have been published this far: the CEJO framework, which can only be applied to ciphers with small S-boxes, and self-equivalence...

Despite the growing demand for software implementations of ECDSA secure against attackers with full control of the execution environment, the scientific literature on white-box ECDSA design is scarce. To assess the state-of-the-art and encourage practical research on this topic, the WhibOx 2021 contest invited developers to submit white-box ECDSA implementations and attackers to break the corresponding submissions. In this work we describe several attack techniques and designs used during...

Cryptography is increasingly deployed in applications running on open devices in which the software is extremely vulnerable to attacks, since the attacker has complete control over the execution platform and the software implementation itself. This creates a challenge for cryptography: design implementations of cryptographic algorithms that are secure, not only in the black-box model, but also in this attack context that is referred to as the white-box adversary model. Moreover, emerging...

The SM4 block cipher was first released in 2006 as SMS4 used in the Chinese national standard WAPI, and became a Chinese national standard in 2016 and an ISO international standard in 2021. White-box cryptography aims primarily to protect the secret key used in a cryptographic software implementation in the white-box scenario that assumes an attacker to have full access to the execution environment and execution details of an implementation. Since white-box cryptography has many real-life...

How much computational resource do we need for cryptography? This is an important question of both theoretical and practical interests. In this paper, we study the problem on pseudorandom functions (PRFs) in the context of circuit complexity. Perhaps surprisingly, we prove extremely tight upper and lower bounds in various circuit models. * In general $B_2$ circuits, assuming the existence of PRFs, PRFs can be constructed in $2n + o(n)$ size, simplifying and improving the $O(n)$ bound by...

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...

White-box cryptography challenges the assumption that the endpoints are trusted and aims at providing protection against an adversary more powerful than the one in the traditional black-box cryptographic model. 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 has read-only access to data with a size bounded by a space-hardness parameter...

White-box cryptography has been proposed as a software protection technique for applications where limited or no hardware-based security is available. In recent years it has been crucial for enabling the security of mobile payment applications. In this paper we continue a recent line of research on device binding for white-box cryptography. Device binding ensures that a white-box program is only executable on one specific device and is unusable elsewhere. Building on this, we ask the...

White-box cryptography is often used in embedded applications. Although white-box cryptography with provable security has been proposed recently, the circuit size is much larger than that of usual block ciphers. We address this problem in a different way from previous works. In particular, we propose a white-box symmetric cipher using quantum memory. The size of our cipher is a polynomial in input-length and output-length of an underlying function. The security against classical attacks is...

Zero-knowledge succinct non-interactive arguments (zk-SNARKs) rely on knowledge assumptions for their security. Meanwhile, as the complexity and scale of cryptographic systems continues to grow, the composition of secure protocols is of vital importance. The current gold standards of composable security, the Universal Composability and Constructive Cryptography frameworks cannot capture knowledge assumptions, as their core proofs of composition prohibit white-box extraction. In this paper,...

We present an approach for designing fast public key encryption cryptosystems using random primitives and error permutation. An encryption speed of such systems allows to use them for “on-the-fly” public key encryption and makes them useful for real-time communications. A small error size allows to use this approach for designing digital signature schemes

Private Stream Aggregation (PSA) protocols allow for the secure aggregation of time-series data, affording security and privacy to users' private data, with significantly better efficiency than general secure computation such as homomorphic encryption, multiparty computation, and secure hardware based approaches. Earlier PSA protocols face limitations including needless complexity, a lack of post-quantum security, or other practical issues. In this work, we present SLAP, a Simple...

All academic methods to secure software implementations of block ciphers against adversaries with full control of the device have been broken. Despite the huge progress in the cryptanalysis of these white-box implementations, no recent progress has been made on the design side. Most of the white-box designs follow the CEJO framework, where each round is encoded by composing it with small random permutations. While several generic attacks have been proposed on the CEJO framework, no generic...

The aim of white-box cryptography is to protect a secret key in a whitebox environment in which an adversary has full control ability over the computer’s execution process and the running environment. In order to solve the issues of lower security in static white-box algorithm and inconvenient application in traditional dynamic white-box algorithm, it is proposed that a white-box block cipher scheme based on dynamic library named WBCD. In this scheme, look-up tables and affine...

This article presents a proposal for an asymmetric white-box scheme. While symmetric white-box is a well studied topic (in particular for AES white-box) with a rich literature, there is almost no public article on the topic of asymmetric white-box. However, asymmetric white-box designs are used in practice by the industry and are a real challenge. Proprietary implementations can be found in the wild but are usually heavily obfuscated and their design is not public, which makes their study...

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 ...

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...

In 2017, the first CHES Capture the Flag Challenge was organized in an effort to promote good design candidates for white-box cryptography. In particular, the challenge assessed the security of the designs with regard to key extraction attacks. A total of 94 candidate programs were submitted, and all of them were broken eventually. Even though most candidates were broken within a few hours, some candidates remained robust against key extraction attacks for several days, and even weeks. In...

White-box cryptography is a software technique to protect secret keys of cryptographic algorithms from attackers who have access to memory. By adapting techniques of differential power analysis to computation traces consisting of runtime information, Differential Computation Analysis (DCA) has recovered the secret keys from white-box cryptographic implementations. In order to thwart DCA, a masked white-box implementation has been suggested. However, each byte of the round output was not...

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...

White-box cryptography was first introduced by Chow et al. in $2002$ as a software technique for implementing cryptographic algorithms in a secure way that protects secret keys in an untrusted environment. Ever since, Chow et al.'s design has been subject to the well-known Differential Computation Analysis (DCA). To resist DCA, a natural approach that white-box designers investigated is to apply the common side-channel countermeasures such as masking. In this paper, we suggest applying the...

The goal of white-box cryptography is to provide security even when the cryptographic implementation is executed in adversarially controlled environments. White-box implementations nowadays appear in commercial products such as mobile payment applications, e.g., those certified by Mastercard. Interestingly, there, white-box cryptography is championed as a tool for secure storage of payment tokens, and importantly, the white-boxed storage functionality is bound to a hardware functionality to...

White-box cryptography was originally introduced in the setting of digital rights management with the goal of preventing a user from illegally re-distributing their software decryption program. In recent years, mobile payment has become a popular new application for white-box cryptography. Here, white-box cryptography is used to increase the robustness against external adversaries (i.e., not the user) who aim to misuse/attack the cryptographic functionalities of the payment application. A...

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...

Linear transformations are applied to the white-box cryptographic implementation for the diffusion effect to prevent key-dependent intermediate values from being analyzed. However, it has been shown that there still exists a correlation before and after the linear transformation, and thus this is not enough to protect the key against statistical analysis. So far, the Hamming weight of rows in the invertible matrix has been considered the main cause of the key leakage from the linear...

Unlike black-box cryptography, an adversary in a white-box security model has full access to the implementation of the cryptographic algorithm. Thus, white-box implementation of cryptographic algorithms is more practical. Nevertheless, in recent years, there is no white-box implementation for public key cryptography. In this paper, we propose 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...

The goal of white-box cryptography is to implement cryptographic algorithms securely in software in the presence of an adversary that has complete access to the software's program code and execution environment. In particular, white-box cryptography needs to protect the embedded secret key from being extracted. As for today, all publicly available white-box implementations turned out succeptible to key extraction attacks. In the meanwhile, white-box cryptography is widely deployed in...

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...

In traditional symmetric cryptography, the adversary has access only to the inputs and outputs of a cryptographic primitive. In the white-box model the adversary is given full access to the implementation. He can use both static and dynamic analysis as well as fault analysis in order to break the cryptosystem, e.g. to extract the embedded secret key. Implementations secure in such model have many applications in industry. However, creating such implementations turns out to be a...

Digital rights management is an important technique to protect digital contents from abuse. Usually it is confronted with severe challenges because of the untrusted environment its application executed in. This condition is formally described as white-box attack model. White-box cryptography aims at protecting software implementation of cryptographic algorithms from white-box attack, hence can be employed to provide security guarantee for digital rights management. Key extraction, code...

Program obfuscation is a powerful security primitive with many applications. White-box cryptography studies a particular subset of program obfuscation targeting keyed pseudorandom functions (PRFs), a core component of systems such as mobile payment and digital rights management. Although the white-box obfuscators currently used in practice do not come with security proofs and are thus routinely broken, recent years have seen an explosion of \emph{cryptographic} techniques for obfuscation,...

The main efficiency metrics for a cryptographic primitive are its speed, its code size and its memory complexity. For a variety of reasons, many algorithms have been proposed that, instead of optimizing, try to increase one of these hardness forms. We present for the first time a unified framework for describing the hardness of a primitive along any of these three axes: code-hardness, time-hardness and memory-hardness. This unified view allows us to present modular block cipher and sponge...

Despite the fact that all current scientific white-box approaches of standardized cryptographic primitives have been publicly broken, these attacks require knowledge of the internal data representation used by the implementation. In practice, the level of implementation knowledge required is only attainable through significant reverse engineering efforts. In this paper we describe new approaches to assess the security of white-box implementations which require neither knowledge about the...

Recently, gray-box attacks on white-box cryptographic implementations have succeeded. These attacks are more efficient than white-box attacks because they can be performed without detailed knowledge of the target implementation. The success of the gray-box attack is reportedly due to the unbalanced encoding used to generate the white-box lookup table. In this paper, we propose a method to protect the gray-box attack against white-box implementations. The basic idea is to apply the masking...

First-order secure Threshold Implementations (TI) of symmetric cryptosystems provide provable security at a moderate overhead; yet attacks using higher-order statistical moments are still feasible. Cryptographic instances compliant to Higher-Order Threshold Implementation (HO-TI) can prevent such attacks, however, usually at unacceptable implementation costs. As an alternative concept we investigate in this work the idea of dynamic hardware modification, i.e., random changes and...

The security requirement of white-box cryptography (WBC) is that it should protect the secret key from a white-box security model that permits an adversary who is able to entirely control the execution of the cryptographic algorithm and its environment. It has already been demonstrated that most of the WBCs are vulnerable to algebraic attacks from a white-box security perspective. Recently, a new differential computation analysis (DCA) attack has been proposed that thwarts the white-box...

Oblivious transfer protocol is an important cryptographic primitive having numerous applications and particularly playing an essential role in secure multiparty computation protocols. On the other hand existing oblivious transfer protocols are based on computationally expensive public-key operations which remains the main obstacle for employing such protocols in practical applications. In this paper a novel approach for designing oblivious transfer protocols is introduced based on the idea...

White-box cryptography aims at providing security against an adversary that has access to the encryption process. Numerous white-box encryption schemes were proposed since the introduction of white-box cryptography by Chow et al. in 2002. However, most of them are slow, and thus, can be used in practice only to protect very small amounts of information, such as encryption keys. In this paper we present a new threat model for white-box cryptography which corresponds to the practical...

In recent years there have been several attempts to build white-box block ciphers whose implementation aims to be incompressible. This includes the weak white-box ASASA construction by Bouillaguet, Biryukov and Khovratovich from Asiacrypt 2014, and the recent space-hard construction by Bogdanov and Isobe at CCS 2016. In this article we propose the first constructions aiming at the same goal while offering provable security guarantees. Moreover we propose concrete instantiations of our...

Implementations of white-box cryptography aim to protect a secret key in a white-box environment in which an adversary has full control over the execution process and the entire environment. Its fundamental principle is the map of the cryptographic architecture, including the secret key, to a number of encoded tables that shall resist the inspection and decomposition of an attacker. In a gray-box scenario, however, the property of hiding required implementation details from the attacker...

We analyse and dene practical requirements in white-box attack environment, and then propose secure and eective cryptographic constructions combining WBC primitive and standard block cipher, pro- viding security and reasonable performance. The proposed design also delivers great eectiveness in the commercial development of crypto- graphic systems, transforming the existing cryptographic libraries secure in the black-box model to those secure in the white-box model. Further- more, the...

Although all current scientific white-box approaches of standardized cryptographic primitives are broken, there is still a large number of companies which sell "secure" white-box products. In this paper a new approach to assess the security of white-box implementations is presented which requires neither knowledge about the look-up tables used nor any reverse engineering effort. This differential computation analysis (DCA) attack is the software counterpart of the differential power analysis...

The ASASA construction is a new design scheme introduced at Asiacrypt 2014 by Biryukov, Bouillaguet and Khovratovich. Its versatility was illustrated by building two public-key encryption schemes, a secret-key scheme, as well as super S-box subcomponents of a white-box scheme. However one of the two public-key cryptosystems was recently broken at Crypto 2015 by Gilbert, Plût and Treger. As our main contribution, we propose a new algebraic key-recovery attack able to break at once the...

We consider the problem of recovering the internal specification of a general SP-network consisting of three linear layers (A) interleaved with two Sbox layers (S) (denoted by ASASA for short), given only black-box access to the scheme. The decomposition of such general ASASA schemes was first considered at ASIACRYPT 2014 by Biryukov et al. which used the alleged difficulty of this problem to propose several concrete block cipher designs as candidates for white-box cryptography. In this...

White-box cryptography is an obfuscation technique for protecting secret keys in software implementations even if an adversary has full access to the implementation of the encryption algorithm and full control over its execution platforms. This concept was presented by Chow et al. with white-box implementations of DES and AES in 2002. The strategy used in the implementations has become a design principle for subsequent white-box implementations. However, despite its practical importance,...

In this paper we pick up an old challenge to design public key or white-box construction from symmetric cipher components. We design several encryption schemes based on the \textsf{ASASA} structure ranging from fast and generic symmetric ciphers to compact public key and white-box constructions based on generic affine transformations combined with specially designed low degree non-linear layers. While explaining our design process we show several instructive attacks on the weaker variants of...

White-box cryptography has attracted a growing interest from researchers in the last decade. Several white-box implementations of standard block-ciphers (DES, AES) have been proposed but they have all been broken. On the other hand, neither evidence of existence nor proofs of impossibility have been provided for this particular setting. This might be in part because it is still quite unclear what {white-box} cryptography really aims to achieve and which security properties are expected from...

The goal of white-box cryptography is to design implementations of common cryptographic algorithm (e.g. AES) that remain secure against an attacker with full control of the implementation and execution environment. This concept was put forward a decade ago by Chow et al. (SAC 2002) who proposed the first white-box implementation of AES. Since then, several works have been dedicated to the design of new implementations and/or the breaking of existing ones. In this paper, we describe a new...

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...

White-box cryptography concerns the design and analysis of implementations of cryptographic algorithms engineered to execute on untrusted platforms. Such implementations are said to operate in a \emph{white-box attack context}. This is an attack model where all details of the implementation are completely visible to an attacker: not only do they see input and output, they see every intermediate computation that happens along the way. The goal of a white-box attacker when targeting...

The method of concealing a linear relationship between elements of a finite field (LRC method) is described. An LRC method based approach to the secure white-box implementations creating problem is considered. SPN cipher characteristics to create its secure White-Box implementation are revealed.

Protecting an implementation against Side Channel Analysis for Reverse Engineering (SCARE) attacks is a great challenge and we address this challenge by presenting a first proof of concept. White-box cryptography has been developed to protect programs against an adversary who has full access to their software implementation. It has also been suggested as a countermeasure against side channel attacks and we examine here these techniques in the wider perspective of SCARE. We consider that the...

A key research question in computer security is whether one can implement software that offers some protection against software attacks from its execution platform. While code obfuscation attempts to hide certain characteristics of a program P, white-box cryptography specifically focusses on software implementations of cryptographic primitives (such as encryption schemes); the goal of a white-box implementation is to offer a certain level of robustness against an adversary who has full...

A white-box implementation of a block cipher is a software implementation from which it is difficult for an attacker to extract the cryptographic key. Chow et al. published white-box implementations for AES and DES that both have been cryptanalyzed. However, these white-box implementations are based on ideas that can easily be used to derive white-box implementations for other block ciphers as well. As the cryptanalyses published use typical properties of AES and DES, it remains an open...

At DRM 2002, Chow et al. presented a method for implementing the DES block cipher such that it becomes hard to extract the embedded secret key in a white-box attack context. In such a context, an attacker has full access to the implementation and its execution environment. In order to provide an extra level of security, an implementation shielded with external encodings was introduced by Chow et al. and improved by Link and Neumann. In this paper, we present an algorithm to extract the...

Obfuscation is a method consisting in hiding information of some parts of a computer program. According to the Kerckhoffs principle, a cryptographical algorithm should be kept public while the whole security should rely on the secrecy of the key. In some contexts, source codes are publicly available, while the key should be kept secret; this is the challenge of code obfuscation. This paper deals with the cryptanalysis of such methods of obfuscation applied to the DES. Such methods, called...

At CMS 2006 Bringer et al. show how to conceal the algebraic structure of a ``traceable block cipher'' by adding perturbations to its description. We here exploit and strengthen their ideas by further perturbing the representation of a cipher towards a white box implementation. Our technique is quite general, and we apply it -- as a challenging example in the domain of white box cryptography -- to a variant of the block cipher AES.