Security analysis of Subterranean 2.0

Abstract

Subterranean 2.0 is a cipher suite that can be used for hashing, authenticated encryption, MAC computation, etc. It was designed by Daemen, Massolino, Mehrdad, and Rotella, and has been selected as a candidate in the second round of NIST’s lightweight cryptography standardization process. Subterranean 2.0 is a duplex-based construction and utilizes a single-round permutation in the duplex. It is the simplicity of the round function that makes it an attractive target of cryptanalysis. In this paper, we examine the single-round permutation in various phases of Subterranean 2.0 and specify three related attack scenarios that deserve further investigation: keystream biases in the keyed squeezing phase, state collisions in the keyed absorbing phase, and one-round differential analysis in the nonce-misuse setting. To facilitate cryptanalysis in the first two scenarios, we novelly propose a set of size-reduced toy versions of Subterranean 2.0: Subterranean-m. Then we make an observation for the first time on the resemblance between the non-linear layer in the round function of Subterranean 2.0 and SIMON’s round function. Inspired by the existing work on SIMON, we propose explicit formulas for computing the exact correlation of linear trails of Subterranean 2.0 and other ciphers utilizing similar non-linear operations. We then construct our models for searching trails to be used in the keystream bias evaluation and state collision attacks. Our results show that most instances of Subterranean-m are secure in the first two attack scenarios but there exist instances that are not. Further, we find a flaw in the designers’ reasoning of Subterranean 2.0’s linear bias but support the designers’ claim that there is no linear bias measurable from at most $$2^{96}$$ 2 96 data blocks. Due to the time-consuming search, the security of Subterranean 2.0 against the state collision attack in keyed modes still remains an open question. Finally, we observe that one-round differentials allow to recover state bits in the nonce-misuse setting. By proposing nested one-round differentials, we obtain a sufficient number of state bits, leading to a practical state recovery with only 20 repetitions of the nonce and 88 blocks of data. It is noted that our work does not threaten the security of Subterranean 2.0.

Differential Trail Search in Cryptographic Primitives with Big-Circle Chi:

“…Related work. We conclude by briefly discussing the relation of our work with the one recently proposed by Song et al in [STSH21]. First of all, in there, authors propose several attacks on different primitives of Subterranean based on one-round differentials, on the contrary, we investigated 8 rounds of Subterranean.…”

“…Besides this, in [STSH21], authors pointed out that the χ function in Subterranean can be re-written as the non-linear layer of SIMON [BSS + 13], a family of lightweight block ciphers proposed by Beaulieu et al Its round function contains (x ≪ α) • (x ≪ β) + (x ≪ γ), where x ≪ i indicates the cyclic left shift over i bits, while the χ function in Subterranean can be re-written as x + (x ≫ 1) • (x ≫ 2) + (x ≫ 2) where x ≫ i indicates the cyclic right shift over i bits. This suggests that the techniques for searching differential trails of SIMON can be potentially applied to Subterranean as well.…”