Cryptology ePrint Archive: Report 2014/652

A Dynamic Cube Attack on $105$ round Grain v1

Subhadeep Banik

Abstract: As far as the Differential Cryptanalysis of reduced round Grain v1 is concerned, the best results were those published by Knellwolf et al. in Asiacrypt $2011$. In an extended version of the paper, it was shown that it was possible to retrieve {\bf (i)} $5$ expressions in the Secret Key bits for a variant of Grain v1 that employs $97$ rounds (in place of $160$) in its Key Scheduling process using $2^{27}$ chosen IVs and {\bf (ii)} $1$ expression in Secret Key bits for a variant that employs $104$ rounds in its Key Scheduling using $2^{35}$ chosen IVs. However, the second attack on $104$ rounds, had a success probability of around $50$\%, which is to say that the attack worked for only around one half of the Secret Keys.

In this paper we propose a dynamic cube attack on $105$ round Grain v1, that has a success probability of $100$\%, and thus we report an improvement of $8$ rounds over the previous best attack on Grain v1 that attacks the entire Keyspace. We take the help of the tool $\Delta${\sf Grain}$_{\sf KSA}$, proposed by Banik at ACISP 2014, to track the differential trails induced in the internal state of Grain v1 by any difference in the IV bits, and we prove that a suitably introduced difference in the IV leads to a distinguisher for the output bit produced in the $105^{th}$ round. This, in turn, helps determine the values of $6$ expressions in the Secret Key bits.

Category / Keywords: secret-key cryptography / eStream, Differential Cryptanalysis, Dynamic Cube Attack, Grain v1, Stream Cipher.

Date: received 22 Aug 2014

Contact author: subb at dtu dk

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Version: 20140827:073916 (All versions of this report)

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