Related-Key Chosen IV Attacks on Grain-v1 and Grain-128
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
A framework for chosen IV statistical analysis of stream ciphers
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Chosen IV statistical analysis for key recovery attacks on stream ciphers
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Analysis of Grain's initialization algorithm
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Breaking Grain-128 with dynamic cube attacks
FSE'11 Proceedings of the 18th international conference on Fast software encryption
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
An experimentally verified attack on full grain-128 using dedicated reconfigurable hardware
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
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In this paper we explain how one can obtain Key-IV pairs for Grain family of stream ciphers that can generate output key-streams which are either (i) almost similar in the initial part or (ii) exact shifts of each other throughout the generation of the stream. Let lP be the size of the pad used during the key loading of Grain. For the first case, we show that in expected $2^{l_P}$ many invocations of the Key Scheduling Algorithm and its reverse routine, one can obtain two related Key-IV pairs that can produce same output bits in 75 (respectively 112 and 115) selected positions among the initial 96 (respectively 160 and 160) bits for Grain v1 (respectively Grain-128 and Grain-128a). Similar idea works for the second case in showing that given any Key-IV, one can obtain another related Key-IV in expected $2^{l_P}$ many trials such that the related Key-IV pairs produce shifted key-streams. We also provide an efficient strategy to obtain related Key-IV pairs that produce exactly i-bit shifted key-streams for small i. Our technique pre-computes certain equations that help in obtaining such related Key-IV pairs in 2i many expected trials.