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I’m reading this paper of Lai and Massey where they give a very nice perspective on differential attacks in general

http://www.isiweb.ee.ethz.ch/papers/arch/xlai-mass-inspec-1991-3.pdf

They do their analysis with a general group operation (see Definition on pg 6) which is classically taken as XOR.

Have any ciphers been broken with a group operation other than XOR which can’t be broken by the classical differential? I’m after things independent of using higher order differentials.

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