DLCT: A new tool for differential-linear cryptanalysis

Differential cryptanalysis and linear cryptanalysis are the two best-known techniques for cryptanalysis of block ciphers. In 1994, Langford and Hellman introduced the differential-linear (DL) attack based on dividing the attacked cipher E into two subciphers E₀ and E₁ and combining a differential characteristic for E₀ with a linear approximation for E₁ into an attack on the entire cipher E. The DL technique was used to mount the best known attacks against numerous ciphers, including the AES finalist Serpent, ICEPOLE, COCONUT98, Chaskey, CTC2, and 8-round DES. Several papers aimed at formalizing the DL attack, and formulating assumptions under which its complexity can be estimated accurately. These culminated in a recent work of Blondeau, Leander, and Nyberg (Journal of Cryptology, 2017) which obtained an accurate expression under the sole assumption that the two subciphers E₀ and E₁ are independent. In this paper we show that in many cases, dependency between the two subcipher s significantly affects the complexity of the DL attack, and in particular, can be exploited by the adversary to make the attack more efficient. We present the Differential-Linear Connectivity Table (DLCT) which allows us to take into account the dependency between the two subciphers, and to choose the differential characteristic in E₀ and the linear approximation in E₁ in a way that takes advantage of this dependency. We then show that the DLCT can be constructed efficiently using the Fast Fourier Transform. Finally, we demonstrate the strength of the DLCT by using it to improve differential-linear attacks on ICEPOLE and on 8-round DES, and to explain published experimental results on Serpent and on the CAESAR finalist Ascon which did not comply with the standard differential-linear framework.