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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 $QRP \ge_P FACTORING$?

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I would put it as "it is conjectured" rather than "it is assumed", but otherwise, yeah...

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