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Sbox(x 1 ? x 2 ? x 3 ? i) ? (y 1 ? y 2 ? y 3 ), Sbox ,
Sbox(x 1 ? x 2 ? x 3 ? i) ? (y 1 ? y 2, Sbox(x 1 ? x 2 ? x 3 ? j) ? (y 1 ? y 2 )) ,
By summing the second and third variables, the attacker obtains Sbox(x 1 ? x 2 ? x 3 ? i) ? Sbox(x 1 ? x 2 ? x 3 ? j) The additional knowledge of x 0 clearly breaks the independence from X. To recover secrets from a set of observations of the second type, the attacker can sum the second and third variables to obtain x 1 ? x 2 ? x 3 , from which he can learn y 1 ? y 2 ? y 3 (by combining it with the second variable) and then Y (by combining it with the first one). The third family is a variant of the first: the Sbox masks can be removed in both cases. Finally, when observing three variables in the fourth family of observations, the knowledge of both x 0 and y 0 unmasks the third observed variable, p.142 ,
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