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Title:
More NTRU+Sign Signatures from Cyclotomic Trinomials
Authors: Ga Hee Hong, Joo Woo, Jonghyun Kim, Minku Kim, Hochang Lee, Jong Hwan Park
Abstract:Recently, \mathsf{NTRU}+\mathsf{Sign} was proposed as a new compact signature scheme, following `Fiat-Shamir with Aborts’ (FSwA) framework. Its compactness is mainly based on their novel NTRU-based key structure that fits well with bimodal distributions in the FSwA framework. However, despite its compactness, \mathsf{NTRU}+\mathsf{Sign} fails to provide a diverse set of parameters that can meet some desired security levels. This limitation stems from its reliance on a ring \mathbb{Z}_q[x]/\langle x^n+1 \rangle, where n is restricted to powers of two, limiting the flexibility in selecting appropriate security levels. To overcome this limitation, we propose a revised version of \mathsf{NTRU}+\mathsf{Sign} by adopting a ring \mathbb{Z}_q[x]/\langle x^n-x^{n/2}+1\rangle from cyclotomic trinomials, where n=2^{i}3^{j} for some positive integers i and j. Our parameterization offers three distinct security levels: approximately 120, 190, and 260 bits, while preserving the compactness in \mathbb{Z}_q[x]/\langle x^n+1 \rangle. We implement these re-parameterized \mathsf{NTRU}+\mathsf{Sign} schemes, showing that the performance of \mathsf{NTRU}+\mathsf{Sign} from cyclotomic trinomials is still comparable to previous lattice-based signature schemes such as \mathsf{Dilithium} and \mathsf{HAETAE}.
ePrint: https://eprint.iacr.org/2025/612
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