# Questions tagged [ntru]

NTRU is an encryption algorithm which is based on the shortest vector problem in a lattice.

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### Noncommutative generalizations of NTRU

I recently learned and implemented NTRU Encrypt successfully in Python/SageMath. The key players are the polynomial rings $R = \mathbb{Z}[x]/(x^N-1)$ and reduction $R_p = \mathbb{Z}_p[x]/(x^N-1)$. One ...
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### What are the recommended parameters for NTRUEncrypt?

I'm looking into NTRU for the first time and I am confused by the variants and the set of parameters. I'd like to use a secure NTRU-based cryptosystem to have a (plausibly) quantum secure PKE offering ...
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### Shortest Vector Problem as Dihedral Hidden Subgroup Problem

I’m a mathematician trying to get into cryptography. I have a somewhat silly question, but I can’t seem to find a proper answer anywhere. I am interested in whether or not there is a way to directly ...
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### Canonical inclusion map in subfield attack on overstretched NTRU

I'm trying to understand subfield attacks on overstretched NTRU. In the paper https://eprint.iacr.org/2016/127.pdf authors used "canonical inclusion map" to lift vector to full lattice. What does ...
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### Significance of parameter q in NTRU lattice attack

In NTRU (N,p,q,d), N is usually chosen to be prime and q be a power of 2. Why is it that if I increase the parameter q, the probability of finding a key or spurious key that can decrypt the message is ...
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