Cryptanalysis on Reduced-Round 3D and Saturnin

Abstract3D is an Advanced Encryption Standard (AES)-like cipher employed 3D structure proposed in 2008. The main innovation of 3D is the multi-dimensional state, generalizing the design of Rijndael and allowing block sizes beyond the 256-bit boundary. Saturnin, a lightweight block cipher has been selected as a second-round candidate in the National Institute of Standards and Technology standardization for lightweight cryptography. It also employs a 3D structure and provides high security against quantum and classic attacks. The exchange-equivalence attacks proposed by Bardeh and Rønjom consider how quadruples of plaintexts confirm distinguishable properties for AES. It is similar to the principle of yoyo attack, but it can find a longer number of rounds of distinguisher. In this paper, we investigate the exchange-equivalence attack on 3D and yoyo attack on Saturnin. Our new results turn out to be the first secret-key chosen plaintext distinguisher for 10-round 3D. The complexity of the distinguisher is about $2^{364.2}$ in terms of data, memory and computational complexity. For Saturnin, we propose the first six-super-round impossible differential yoyo attack, which is suitable for the two-S-layer version. Compared with the previous impossible differential attacks in the design report of Saturnin, the attacks presented here are the best in terms of the complexity under the chosen-plaintext scenario.