• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.9
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• pp.4548-4559
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• 2018

Conditional differential attack against NFSR-based cryptosystems proposed by Knellwolf et al. in Asiacrypt 2010 has been widely used for analyzing round-reduced Grain v1. In this paper, we present improved conditional differential attacks on Grain v1 based on a factorization simplification method, which makes it possible to obtain the expressions of internal states in more rounds and analyze the expressions more precisely. Following a condition-imposing strategy that saves more IV bits, Sarkar's distinguishing attack on Grain v1 of 106 rounds is improved to a key recovery attack. Moreover, we show new distinguishing attack and key recovery attack on Grain v1 of 107 rounds with lower complexity O($2^{34}$) and appreciable theoretical success probability 93.7%. Most importantly, our attacks can practically recover key expressions with higher success probability than theoretical results.