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2017 | OriginalPaper | Chapter

Choosing Parameters for NTRUEncrypt

Authors : Jeff Hoffstein, Jill Pipher, John M. Schanck, Joseph H. Silverman, William Whyte, Zhenfei Zhang

Published in: Topics in Cryptology – CT-RSA 2017

Publisher: Springer International Publishing

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Abstract

We describe a method for generating parameter sets, and calculating security estimates, for NTRUEncrypt. Our security analyses consider lattice attacks, the hybrid attack, subfield attacks, and quantum search. Analyses are provided for the IEEE 1363.1-2008 product-form parameter sets, for the NTRU Challenge parameter sets, and for two new parameter sets. These new parameter sets are designed to provide \(\ge 128\)-bit post-quantum security.

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next chapter Encoding-Free ElGamal-Type Encryption Schemes on Elliptic Curves
Footnotes
1
In practice q has a strong impact on the effectiveness of pure lattice reduction attacks as well. For large q the relevant problem becomes Unique-SVP which appears to be somewhat easier than Hermite-SVP. Conservative parameter generation should ensure that it is difficult to solve Hermite-SVP to within a factor of \(q/\varDelta ^{1/2N} = \sqrt{q}\).
 
2
A lattice reduction algorithm that achieves root Hermite factor \(\delta \) returns a basis with \(\Vert {\varvec{b}}_1\Vert _2 \approx \delta ^n \det (\varLambda )^{1/n}\).
 
3
We will abuse notation slightly and allow \(\varPi \) to act on elements of R by acting on their coefficient vectors lifted to \(\mathbb {Z}^N\).
 
4
The \(X_k\) for different k have the same distribution, but they are not completely independent. However, they are so weakly correlated as to not affect our analysis.
 
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Metadata
Title
Choosing Parameters for NTRUEncrypt
Authors
Jeff Hoffstein
Jill Pipher
John M. Schanck
Joseph H. Silverman
William Whyte
Zhenfei Zhang
Copyright Year
2017
Book
Topics in Cryptology – CT-RSA 2017

Print ISBN: 978-3-319-52152-7

Electronic ISBN: 978-3-319-52153-4

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-52153-4_1

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