Improved Security Evaluation of SPN Block Ciphers and its Applications in the Single-key Attack on SKINNY

Abstract

In this paper, a new method for evaluating the integral property, truncated and impossible differentials for substitution-permutation network (SPN) block ciphers is proposed. The main assumption is an explicit description/expression of the internal state words in terms of the plaintext (ciphertext) words. By counting the number of times these words occur in the internal state expression, we can evaluate the resistance of a given block cipher to integral and impossible/truncated differential attacks more accurately than previous methods. More precisely, we explore the cryptographic consequences of uneven frequency of occurrences of plaintext (ciphertext) words appearing in the algebraic expression of the internal state words. This approach gives a new family of distinguishers employing different concepts such as the integral property, impossible/truncated differentials and the so-called zero-sum property. We then provide algorithms to determine the maximum number of rounds of such new types of distinguishers for SPN block ciphers. The potential and efficiency of this relatively simple method is confirmed through applications. For instance, in the case of SKINNY block cipher, several 10-round integral distinguishers, all of the 11-round impossible differentials, and a 7-round truncated differential could be determined. For the last case, using a single pair of plaintexts differing in three words so that (a = b = c) ≠ (a’ = b’ = c’), we are able to distinguish 7-round SKINNY from random permutations. More importantly, exploiting our distinguishers, we give the first practical attack on 11-round SKINNY-128-128 in the single-key setting (a theoretical attack reaches 16 rounds). Finally, using the same ideas, we provide a concise explanation on the existing distinguishers for round-reduced AES.

Conditional differential analysis on the KATAN ciphers based on deep learning

“…Zhang et al. [21] proposed a method to use algebraic expressions to express the dependencies of intermediate states on the outputs. Inspired by this method, the output difference of the 84‐round ciphertext is expressed by the 97‐round ciphertext and subkeys.…”

Improved Conditional Differential Analysis on NLFSR Based Block Cipher KATAN32 with MILP

“…Key-Recovery Attack on 97-Round KATAN32. Inspired by the technique representing the dependence of the intermediate state on the output by an algebraic representation in [34], we give the algebraic representation of the intermediate state using the ciphertext and round keys. Using Equations ( 2) and ( 3), we can get the expression of l t , s t in decryption direction:…”

Constructing the Impossible Differential of Type-II GFN with Boolean Function and Its Application to WARP

“…From the per-SKINNY spective of distinguishing attacks, the cryptanalysts try to construct an impossible differential which covers as many rounds as possible. At EUROCRYPT 2016, Sun et al proved that the upper bound on the length of impossible differentials of substitution-permutation network (SPN) structure by the primitive index of the linear layers [12] without considering the details inside Sboxes. Inspired by this method, Zhang et al evaluated the resistance of SPN block cipher against impossible differential attack by counting the occurrences of the plaintext (ciphertext) words appearing in the expression of the internal state words [13].…”