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In this paper, we analyze the collision resistance of the two smallest versions of Keccak which have a width of 200 and 400 bits respectively. We show that algebraic and linearization techniques can serve collision cryptanalysis by using some interesting properties of the linear part of the round function of Keccak. We present an attack on the Keccak versions that could be used in lightweight cryptography reduced to two rounds. For Keccak[40, 160] (resp. Keccak[72, 128] and Keccak[144, 256]) our attack has a computational complexity of 273 (resp. 252.5 and 2101.5) Keccak calls.

Algebraic Collision Attacks on Keccak