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Anais - Engenharia de Redes de Comunicação - UnB

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• This configuration is not possible.<br />

STEP 3: Determination of the bits on the left si<strong>de</strong> of the central column.<br />

Assume the following notation.<br />

(<br />

α β<br />

δ x<br />

)<br />

=<br />

(<br />

a<br />

t−1<br />

i−1<br />

a t i−1<br />

a t−1<br />

i<br />

x<br />

)<br />

One can easily see that there are 8 different possibilities for the bits {α, β, δ}. Basing<br />

on equation 1, an adversary in possession of the bits {α, β, δ} can <strong>de</strong>termine the bit a t−1<br />

i−2<br />

without applying any fault into the register.<br />

We shall now analyze these 8 possibilities.<br />

Configuration 3.1<br />

(<br />

a<br />

t−1<br />

i−2<br />

a t−1<br />

i−1<br />

a t−1<br />

i<br />

x a t i−1 x<br />

)<br />

=<br />

(<br />

a<br />

t−1<br />

i−2 0 0<br />

x 0 x<br />

)<br />

• This configuration is only possible for a t−1<br />

i−2 = 0.<br />

Configuration 3.2<br />

(<br />

a<br />

t−1<br />

i−2<br />

a t−1<br />

i−1<br />

a t−1<br />

i<br />

x a t i−1 x<br />

)<br />

=<br />

(<br />

a<br />

t−1<br />

i−2 0 0<br />

x 1 x<br />

)<br />

• This configuration is only possible for a t−1<br />

i−2 = 1.<br />

Configuration 3.3<br />

(<br />

a<br />

t−1<br />

i−2<br />

a t−1<br />

i−1<br />

a t−1<br />

i<br />

x a t i−1 x<br />

)<br />

=<br />

(<br />

a<br />

t−1<br />

i−2 1 0<br />

x 0 x<br />

)<br />

• This configuration is only possible for a t−1<br />

i−2 = 1 .<br />

Configuration 3.4<br />

(<br />

a<br />

t−1<br />

i−2<br />

a t−1<br />

i−1<br />

a t−1<br />

i<br />

x a t i−1 x<br />

)<br />

=<br />

(<br />

a<br />

t−1<br />

i−2 1 0<br />

x 1 x<br />

)<br />

• This configuration is only possible for a t−1<br />

i−2 = 0.<br />

Configuration 3.5<br />

(<br />

a<br />

t−1<br />

i−2<br />

a t−1<br />

i−1<br />

a t−1<br />

i<br />

x a t i−1 x<br />

)<br />

=<br />

(<br />

a<br />

t−1<br />

i−2 0 1<br />

x 0 x<br />

)<br />

90

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