A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy ...
A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy ...
A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy ...
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A <strong>Polynomial</strong> <strong>Time</strong> <strong>Algorithm</strong> 221<br />
The system (8) has m 2 variables and (n/2)m 2 equations. However, by precise<br />
analysis of Krammer matrices, we can reduce <strong>the</strong> number of variables and<br />
equations as follows:<br />
Theorem 3. Equation (8) has at most 1 7 n4 nontrivial variables and 1 4 n4 nontrivial<br />
equations.<br />
Proof. Define V k to be a subspace of V 0 generated by {x ij |(i, j) /∈ I k } where<br />
I k = {(i, j)|1 ≤ i
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