Real Time Related Key Attack on Hummingbird-2

Abstract

Hummingbird is a lightweight encryption and message authentication primitive published in RISC’09 and WLC’10. In FSE’11, Markku-Juhani O.Saarinen presented a differential divide-and-conquer method which has complexity upper bounded by 2 64 operations and requires processing of few megabytes of chosen messages under two related nonces (IVs). The improved version, Hummingbird-2, was presented in RFIDSec 2011. Based on the idea of differential collision, this paper discovers some weaknesses of the round function WD16. Combining with the simple key loading algorithm, a related-key chosen-IV attack which can recover the full secret key is proposed. Under 15 pairs of related keys, the 128 bit initial key can be recovered, requiring 2 27 chosen Ⅳ and the computational complexity is O(2 27 ). In average, the attack needs several minutes to recover the full 128-bit secret key on a PC. The experimental result corroborates our attack. The result shows that the Hummingbird-2 cipher can’t resist related key attack.