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For d 6= n=3, or for large k, not all trinary sequences are equally likely, and the adversary may choose to target a small set of high probability sequences Trace) of the public key in some subfield instead of the public key itself. Consequently we must estimate the size of the set of elements that are typical under the projection.

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2.2 private key, blinding polynomial, and message parameters the analysis below will be considerably simpler if we fix how the values d1, d2, d3, and dg will be derived given n and q. The idea consists in decreasing the dimension of the ntru lattice using the multiplication matrix by the norm (resp Key con rmation might be overkill from a security perspective, since a random session key will also produce an authentication failure

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But key con rmation allows the kem to be audited without regard to the authentication mechanism, and adds only 3% to our ciphertext size.

We plot parameter sets for these variants, and parameter sets for streamlined ntru prime, on size of several design decisions If you are looking to use ntruencrypt as opposed to the variant ntruprime, you are probably best advised to use the parameter sets outlined in the submission to the third round of the nist process (as summarised on page 9 of the specification). It appears that the parameter set hps4096821 was added lately to the ntru definition, and did not undergo the same vetting that the other parameter sets did As such, it is unclear whether that parameter set gives the claimed level of security.

Ntru represents a significant improvement in the public key cryptography world—it’s faster, stronger and smaller than virtually any other system in use and it’s quantum computer resistant, making it the best choice for current projects with lifetimes that extend into the post quantum computer age.