International Association
for Cryptologic Research

At EUROCRYPT ’93, Matsui introduced linear cryptanalysis. Both Matsui’s Algorithm 1 and 2 use a linear approximation involving certain state bits. Algorithm 2 requires partial encryptions or decryptions to obtain these state bits after guessing extra key bits. For ciphers where only part of the state can be obtained, like some stream ciphers and authenticated encryption schemes, Algorithm 2 will not work efficiently since it is hard to implement partial encryptions or decryptions. In this case, Algorithm 1 is a good choice since it only involves these state bits, and one bit of key information can be recovered using a single linear approximation trail. However, when there are several strong trails containing the same state bits, known as the linear hull effect, recovering key bits with Algorithm 1 is infeasible. To overcome this, Röck and Nyberg extended Matsui’s Algorithm 1 to linear hulls. However, Röck and Nyberg found that their theoretical estimates are quite pessimistic for low success probabilities and too optimistic for high success probabilities. To deal with this, we construct new statistical models where the theoretical success probabilities are in a good accordance with experimental ones, so that we provide the first accurate analysis of the extension of Matsui’s Algorithm 1 to linear hulls. To illustrate the usefulness of our new models, we apply them to one of the ten finalists of the NIST Lightweight Cryptography (LWC) Standardization project: TinyJAMBU. We provide the first cryptanalysis under the nonce-respecting setting on the full TinyJAMBU v1 and the round-reduced TinyJAMBU v2, where partial key bits are recovered. Our results do not violate the security claims made by the designers.

Statistical saturation attack takes advantage of a set of plaintext with some bits fixed while the others vary randomly, and then track the evolution of a non-uniform plaintext distribution through the cipher. Previous statistical saturation attacks are all implemented under single-key setting, and there is no public attack models under related-key/tweak setting. In this paper, we propose a new cryptanalytic method which can be seen as related-key/tweak statistical saturation attack by revealing the link between the related-key/tweak statistical saturation distinguishers and KDIB (Key Difference Invariant Bias) / TDIB (Tweak Difference Invariant Bias) ones. KDIB cryptanalysis was proposed by Bogdanov et al. at ASIACRYPT’13 and utilizes the property that there can exist linear trails such that their biases are deterministically invariant under key difference. And this method can be easily extended to TDIB distinguishers if the tweak is also alternated. The link between them provides a new and more efficient way to find related-key/tweak statistical saturation distinguishers in ciphers. Thereafter, an automatic searching algorithm for KDIB/TDIB distinguishers is also given in this paper, which can be implemented to find word-level KDIB distinguishers for S-box based key-alternating ciphers. We apply this algorithm to QARMA-64 and give related-tweak statistical saturation attack for 10-round QARMA-64 with outer whitening key. Besides, an 11-round attack on QARMA-128 is also given based on the TDIB technique. Compared with previous public attacks on QARMA including outer whitening key, all attacks presented in this paper are the best ones in terms of the number of rounds.