Compact and Efficient NTRU-based KEM with Scalable Ciphertext Compression
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The NTRU lattice is a promising candidate to construct practical cryptosystems resistant to quantum computing attacks, and particularly plays a leading role in the ongoing NIST post-quantum cryptography standardization. On the one hand, it is benefited from a strong security guarantee since it has essentially not been broken over 24 years. On the other hand, all the known patent threats against NTRU have expired, which is deemed a critical factor for consideration when deploying PQC algorithms in reality. Nevertheless, there are still some obstacles to the computational efficiency and bandwidth complexity of NTRU-based constructions of key encapsulation mechanisms (KEM). To address these issues, we propose a compact and efficient KEM based on the NTRU lattice, called CTRU, by introducing a scalable ciphertext compression technique. It demonstrates a new approach to decrypting NTRU ciphertext, where the plaintext message is recovered with the aid of our decoding algorithm in the scalable E_8 lattice. The instantiation of CTRU is over the NTT-friendly rings of the form ℤ_q[x]/(x^n-x^n/2+1). To our knowledge, our CTRU is the most bandwidth efficient KEM based on the NTRU lattice up to now. In addition, compared to other NTRU-based KEM schemes, CTRU has stronger security against known attacks, enjoys more robust CCA security reduction (starting from IND-CPA rather than OW-CPA), and its encapsulation and decapsulation processes are also among the most efficient. When compared to the NIST Round 3 finalist NTRU-HRSS, our CTRU-768 has 15% smaller ciphertext size and its security is strengthened by (45,40) bits for classical and quantum security respectively. When compared to the NIST Round 3 finalist Kyber that is based on the Module-LWE assumption, CTRU has both smaller bandwidth and lower error probabilities at about the same security level.
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