Compact and efficient KEMs over NTRU lattices

The NTRU lattice is a promising candidate to construct practical cryptosystems, in particular key encapsulation mechanism (KEM), resistant to quantum computing attacks. Nevertheless, there are still some inherent obstacles to NTRU-based KEM schemes when considering integrated performance, taking security, bandwidth, error probability, and computational efficiency as a whole, that is as good as and even better than their {R,M}LWE-based counterparts. In this work, we address the challenges by presenting a new family of NTRU-based KEM schemes, denoted as CTRU and CNTR. By bridging low-dimensional lattice codes and high-dimensional NTRU-lattice-based cryptography with careful design and analysis, to the best of our knowledge, CTRU and CNTR are the first NTRU-based KEM schemes featuring scalable ciphertext compression via only one single ciphertext polynomial, and are the first that can outperform {R,M}LWE-based KEM schemes in terms of integrated performance. For instance, when compared to Kyber, the only KEM scheme currently standardized by NIST, our recommended parameter set CNTR-768 exhibits approximately 12% smaller ciphertext size, when its security is strengthened by $(8,7)$ bits for classical and quantum security respectively, with a significantly lower error probability ($2^{-230}$ for CNTR-768 vs. $2^{-164}$ for Kyber-768). In terms of the state-of-the-art AVX2 implementation of Kyber-768, CNTR-768,achieves a speedup of 2.7X in KeyGen, 3.3X in Encaps, and 1.6X in Decaps, respectively. When compared to the NIST Round 3 finalist NTRU-HRSS, CNTR-768,features 15% smaller ciphertext size, coupled with an improvement of $(55,49)$ bits for classical and quantum security respectively. As for the AVX2 implementation, CNTR-768,outperforms NTRU-HRSS by 26X in KeyGen, 3.0X in Encaps, and 2.2X in Decaps, respectively. Along the way, we develop new techniques for more accurate error probability analysis, and a unified number theoretic transform (NTT) implementation for multiple parameter sets, which may be of independent interest.