Paper 2012/233

A Cryptanalysis of HummingBird-2: The Differential Sequence Analysis

Qi Chai and Guang Gong

Abstract

Hummingbird-2 is one recent design of lightweight block ciphers targeting constraint devices, which not only enables a compact hardware implementation and ultra-low power consumption but also meets the stringent response time as specified in ISO18000-6C. In this paper, we present the first cryptanalytic result on the full version of this cipher using two pairs of related keys, i.e., four keys. We discover that the differential sequences for the last invocation of the round function can be computed by running the full cipher, due to which the search space for the key can be reduced. Base upon this observation, we propose a probabilistic attack encompassing two phases, preparation phase and key recovery phase. The preparation phase, requiring $2^{80}$ effort in time, aims to reach an internal state, with $0.5$ success probability, that satisfies particular conditions. In the key recovery phase, by attacking the last invocation of the round function of the encryption (decryption resp.) using the proposed differential sequence analysis (DSA), we are able to recover $36$ bits (another $44$ bits resp.) of the $128$-bit key. In addition, the remaining $48$ bits of the key can be exhaustively searched and the overall time complexity of the key recovery phase is $2^{48.14}$. Note that the proposed attack, though exhibiting an interesting tradeoff between the success probability and time complexity, is only of a theoretical interest at the moment and does not affect the security of the Hummingbird-2 in practice.