The white box attack context as described in [1, 2] is the common setting where cryptographic software is executed in an untrusted environment—ie an attacker has gained access to the implementation of cryptographic algorithms, and can observe or manipulate the dynamic execution of whole or part of the algorithms. In this paper, we present an efficient practical attack against the obfuscated AES implementation [1] proposed at SAC 2002 as a means to protect AES software operated in the white box context against key exposure. We explain in details how to extract the whole AES secret key embedded in such a white box AES implementation, with negligible memory and worst time complexity 230.

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Cryptanalysis of a white box AES implementation

In this paper we classify all optimal 4 bit S-boxes. Remarkably, up to affine equivalence, there are only 16 different optimal S-boxes. This observation can be used to efficiently generate optimal S-boxes fulfilling additional criteria. One result is that an S-box which is optimal against differential and linear attacks is always optimal with respect to algebraic attacks as well. We also classify all optimal S-boxes up to the so called CCZ equivalence. We furthermore generated all S-boxes fulfilling the conditions on nonlinearity and uniformity for S-boxes used in the block cipher Serpent. Up to a slightly modified notion of equivalence, there are only 14 different S-boxes. Due to this small number it is not surprising that some of the S-boxes of the Serpent cipher are linear equivalent. Another advantage of our characterization is that it eases the highly non-trivial task of choosing good S-boxes for hardware dedicated ciphers a lot.

On the Classification of 4 Bit S-Boxes

Block ciphers encrypt blocks of plaintext, messages, into blocks of ciphertext under the action of a secret key, and the process of encryption is reversed by decryption which uses the same user-supplied key. Block ciphers are fundamental to modern cryptography, in fact they are the most widely used cryptographic primitive useful in their own right, and in the construction of other cryptographic mechanisms. In this book the authors provide a technically detailed, yet readable, account of the state of the art of block cipher analysis, design, and deployment. The authors first describe the most prominent block ciphers and give insights into their design. They then consider the role of the cryptanalyst, the adversary, and provide an overview of some of the most important cryptanalytic methods. The book will be of value to graduate and senior undergraduate students of cryptography and to professionals engaged in cryptographic design. An important feature of the presentation is the authors' exhaustive bibliography of the field, each chapter closing with comprehensive supporting notes.

The Block Cipher Companion

The linear layer is a core component in any substitution-permutation network block cipher. Its design significantly influences both the security and the efficiency of the resulting block cipher. Surprisingly, not many general constructions are known that allow to choose trade-offs between security and efficiency. Especially, when compared to Sboxes, it seems that the linear layer is crucially understudied. In this paper, we propose a general methodology to construct good, sometimes optimal, linear layers allowing for a large variety of trade-offs. We give several instances of our construction and on top underline its value by presenting a new block cipher. PRIDE is optimized for 8-bit micro-controllers and significantly outperforms all academic solutions both in terms of code size and cycle count.

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Block Ciphers – Focus on the Linear Layer (feat. PRIDE)

In order to protect AES software running on untrusted platforms, Chow et al. (2002) designed a white-box implementation. However, Billet et al. (2004) showed that the secret key can be extracted with a time complexity of 230. In this paper, we present an improved whitebox implementation of AES. We use dual ciphers to modify the state and key representations in each round as well as two of the four classical AES operations, SubBytes and MixColumns. We show that, with 61200 possible dual ciphers the complexity of Billet et al. attack is raised to 291. Interestingly, our white-box implementation does not require more memory space than that of Chow et al. implementation.

Protecting white-box AES with dual ciphers

This paper presents two algorithms for solving the linear and the affine equivalence problem for arbitrary permutations (S-boxes). For a pair of n × n-bit permutations the complexity of the linear equivalence algorithm (LE) is O(n32n). The affine equivalence algorithm (AE) has complexity O(n322n). The algorithms are efficient and allow to study linear and affine equivalences for bijective S-boxes of all popular sizes (LE is efficient up to n ≤ 32). Using these tools new equivalent representations are found for a variety of ciphers: Rijndael, DES, Camellia, Serpent, Misty, Kasumi, Khazad, etc. The algorithms are furthermore extended for the case of non-bijective n to m-bit S-boxes with a small value of |n - m| and for the case of almost equivalent S-boxes. The algorithms also provide new attacks on a generalized Even-Mansour scheme. Finally, the paper defines a new problem of S-box decomposition in terms of Substitution Permutations Networks (SPN) with layers of smaller S-boxes. Simple information-theoretic bounds are proved for such decompositions.

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Christophe De Cannièere

Papers

A toolbox for cryptanalysis: linear and affine equivalence algorithms