Improved Information Set Decoding - Decoding Random Linear ...
Improved Information Set Decoding - Decoding Random Linear ...
Improved Information Set Decoding - Decoding Random Linear ...
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Scenario (Bounded Distance <strong>Decoding</strong>)<br />
Obtain x = c + e with c 2 C and w := wt(e) =<br />
Goal: Find e and thus c = x + e<br />
Consider syndrome s := s(x) = H·x = H·(c+e) = H·e<br />
→ Find linear combination of w columns of H matching s<br />
weight w<br />
n<br />
4 5<br />
d-1<br />
2<br />
n-k<br />
H<br />
= + + =<br />
T(n,k,d)<br />
s<br />
= <br />
n<br />
·<br />
x·<br />
4 5<br />
d-1<br />
2<br />
c<br />
· ·<br />
Brute-Force complexity<br />
w<br />
·<br />
IMPROVED INFORMATION SET DECODING ASIACRYPT 2011 | December 2011, Seoul
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