Paper 2016/461

NTRU Prime: reducing attack surface at low cost

Daniel J. Bernstein, Chitchanok Chuengsatiansup, Tanja Lange, and Christine van Vredendaal


Several ideal-lattice-based cryptosystems have been broken by recent attacks that exploit special structures of the rings used in those cryptosystems. The same structures are also used in the leading proposals for post-quantum lattice-based cryptography, including the classic NTRU cryptosystem and typical Ring-LWE-based cryptosystems. This paper (1) proposes NTRU Prime, which tweaks NTRU to use rings without these structures; (2) proposes Streamlined NTRU Prime, a public-key cryptosystem optimized from an implementation perspective, subject to the standard design goal of IND-CCA2 security; (3) finds high-security post-quantum parameters for Streamlined NTRU Prime; and (4) optimizes a constant-time implementation of those parameters. The resulting sizes and speeds show that reducing the attack surface has very low cost.

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Publication info
Published elsewhere. Major revision.SAC 2017, to appear
post-quantum cryptographypublic-key encryptionlattice-based cryptographyideal latticesNTRURing-LWEsecuritySoliloquyKaratsubasoftware implementationvectorizationfast sorting
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authorcontact-ntruprime @ box cr yp to
2017-08-17: revised
2016-05-13: received
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      author = {Daniel J.  Bernstein and Chitchanok Chuengsatiansup and Tanja Lange and Christine van Vredendaal},
      title = {NTRU Prime: reducing attack surface at low cost},
      howpublished = {Cryptology ePrint Archive, Paper 2016/461},
      year = {2016},
      note = {\url{}},
      url = {}
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