NTRU Prime

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.

NTRU Prime tweaks NTRU to use rings without these structures. Here are two public-key cryptosystems in the NTRU Prime family, both designed for the standard goal of IND-CCA2 security:

sntrup653, sntrup761, sntrup857, ntrulpr653, ntrulpr761, and ntrulpr857 are Streamlined NTRU Prime and NTRU LPRime with high-security post-quantum parameters. sntrup4591761 and ntrulpr4591761 are older versions of sntrup761 and ntrulpr761 using the same mathematical one-way functions. The resulting sizes and Haswell speeds (from the official supercop-20190110 benchmarks for titan0) show that reducing the attack surface has very low cost:

System ciphertext bytes public-key bytes enc cycles dec cycles keygen cycles
sntrup653 897 994 TBA TBA TBA
ntrulpr653 1025 897 TBA TBA TBA
sntrup761 1039 1158 TBA TBA TBA
sntrup4591761 1047 1218 44788 93676 940852
ntrulpr761 1167 1039 TBA TBA TBA
ntrulpr4591761 1175 1047 81144 113708 44948
sntrup857 1184 1322 TBA TBA TBA
ntrulpr857 1312 1184 TBA TBA TBA

Contributors (alphabetical order)


This work was supported by the Netherlands Organisation for Scientific Research (NWO) under grant 639.073.005.

This work was supported by the Commission of the European Communities through the Horizon 2020 program under project number 645622 (PQCRYPTO) and project number 645421 (ECRYPT-CSA).

This work was supported by the U.S. National Science Foundation under grant 1314919. "Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation."

Calculations were carried out on the Saber cluster of the Cryptographic Implementations group at Technische Universiteit Eindhoven.

Version: This is version 2019.04.11 of the "Intro" web page.