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 whitebox speck implementations using self-equivalence encodings. Although we focus on speck in this work, our design could easily be adapted to protect other add-rotate-xor (ARX) ciphers. Then, we analyze the security of our implementation against key-recovery attacks. We propose an algebraic attack to fully recover the master key and external encodings from a white-box speck implementation, with limited effort required. While this result shows that the linear and affine self-equivalences of speck are insecure, we hope that this negative result will spur additional research in higher-degree self-equivalence encodings for white-box cryptography. Finally, we created an open-source Python project implementing our design, publicly available at https://github.com/jvdsn/ white-box-speck. We give an overview of five strategies to generate output code, which can be used to improve the performance of the whitebox implementation. We compare these strategies and determine how to generate the most performant white-box speck code. Furthermore, this project could be employed to test and compare the efficiency of attacks on white-box implementations using self-equivalence encodings.

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 whitebox design strategies have been published this far: the CEJO framework, which can only be applied to ciphers with small S-boxes, and selfequivalence encodings, which were only applied to AES. In this work we propose implicit implementations, a new design of whitebox implementations based on implicit functions, and we show that current generic attacks that break CEJO or self-equivalence implementations are not successful against implicit implementations. The generation and the security of implicit implementations are related to the self-equivalences of the non-linear layer of the cipher, and we propose a new method to obtain self-equivalences based on the CCZ-equivalence. We implemented this method and many other functionalities in a new open-source tool BoolCrypt, which we used to obtain for the first time affine, linear, and even quadratic self-equivalences of the permuted modular addition. Using the implicit framework and these self-equivalences, we describe for the first time a practical white-box implementation of a generic Addition-Rotation-XOR (ARX) cipher, and we provide an opensource tool to easily generate implicit implementations of ARX ciphers.