NTTRU: Truly Fast NTRU Using NTT

Vadim Lyubashevsky, Gregor Seiler
2019 Transactions on Cryptographic Hardware and Embedded Systems  
We present NTTRU – an IND-CCA2 secure NTRU-based key encapsulation scheme that uses the number theoretic transform (NTT) over the cyclotomic ring Z7681[X]/(X768−X384+1) and produces public keys and ciphertexts of approximately 1.25 KB at the 128-bit security level. The number of cycles on a Skylake CPU of our constant-time AVX2 implementation of the scheme for key generation, encapsulation and decapsulation is approximately 6.4K, 6.1K, and 7.9K, which is more than 30X, 5X, and 8X faster than
more » ... se respective procedures in the NTRU schemes that were submitted to the NIST post-quantum standardization process. These running times are also, by a large margin, smaller than those for all the other schemes in the NIST process as well as the KEMs based on elliptic curve Diffie-Hellman. We additionally give a simple transformation that allows one to provably deal with small decryption errors in OW-CPA encryption schemes (such as NTRU) when using them to construct an IND-CCA2 key encapsulation.
doi:10.13154/tches.v2019.i3.180-201 dblp:journals/tches/LyubashevskyS19 fatcat:yeaqxzel6faktg2rzpi5u3f7ku