International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 30 November 2022

Jonghyun Kim, Jong Hwan Park
ePrint Report ePrint Report
NTRU was the first practical public-key encryption scheme constructed on a lattice over a polynomial-based ring, and has been still considered secure against significant cryptanalytic attacks in a few decades. Despite such a long history, NTRU and its variants proposed to date suffer from several drawbacks, such as the difficulty of achieving worst-case correctness error in a moderate modulus, inconvenient sampling distributions for messages, and relatively slower algorithms than other lattice-based schemes.

In this work, we suggest a new NTRU-based key encapsulation mechanism (KEM), called NTRU+, which overcomes almost all existing drawbacks. NTRU+ is constructed based on two new generic transformations called $\mathsf{ACWC}_{2}$ and $\overline{\mathsf{FO}}^{\perp}$. $\mathsf{ACWC}_{2}$ is used for easily achieving a worst-case correctness error, and $\overline{\mathsf{FO}}^{\perp}$ (as a variant of the Fujisaki-Okamoto transform) is used for achieving chosen-ciphertext security without re-encryption. $\mathsf{ACWC}_{2}$ and $\overline{\mathsf{FO}}^{\perp}$ are all defined using a randomness-recovery algorithm and an encoding method. Especially, our simple encoding method, called $\mathsf{SOTP}$, allows us to sample a message from a natural bit-sting space with an arbitrary distribution. We provide four parameter sets for NTRU+ and give implementation results, using NTT-friendly rings over cyclotomic trinomials.
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