Question on the Quadratic Residuosity Assumption I am reading the Handbook of Applied Cryptography and on page 99 the authors write
, after showing that $QRP \le_P FACTORING$:


  It is believed that the $QRP$ is as difﬁcult as the problem of factoring integers, although no proof of this is known.


I am not quite sure what "as difficult" means, do they say that it is assumed that $QRP \ge_P FACTORING$?
I would put it as "it is conjectured" rather than "it is assumed", but otherwise, yeah...