Recovering NTRU Secret Key from Inversion Oracles

We consider the NTRU encryption scheme as lately suggested for use, and study the connection between inverting the NTRU primitive (i.e., the one-way function over the message and the blinding information which underlies the NTRU scheme) and recovering the NTRU secret key (universal breaking). We model the inverting algorithms as black-box oracles and do not take any advantage of the internal ways by which the inversion works (namely, it does not have to be done by following the standard decryption algorithm). This allows for secret key recovery directly from the output on several inversion queries even in the absence of decryption failures. Our oracles might be queried on both valid and invalid challenges e, however they are not required to reply (correctly) when their input is invalid. We show that key recovery can be reduced to inverting the NTRU function. The efficiency of the reduction highly depends on the specific values of the parameters. As a side-result, we connect the collisions of the NTRU function with decryption failures which helps us gain a deeper insight into the NTRU primitive.