This work emphasizes an important problem of braid based cryptography: the random generation of good keys. We present a deterministic, polynomial algorithm that reduces the conjugacy search problem in braid group. The algorithm is based on the decomposition of braids into products of canonical factors and gives a partial factorization of the secret: a divisor and a multiple. The tests we performed on different keys of existing protocols showed that many protocols in their current form are broken and that the efficiency of our attack depends on the random generator used to create the key. Therefore, this method gives new critera for testing weak keys. We also propose a new random generator of key which is secure against our attack and the one of Hofheinz and Steinwandt.

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