The advent of quantum computers poses a significant threat to existing cryptographic systems, thereby affecting the confidentiality and integrity of communications. Among various post-quantum cryptographic schemes, those based on NTRU lattices have achieved considerable success. For example, NTRU-Prime has been implemented in network security protocols such as OpenSSH and OpenBSD, becoming a de facto standard. However, traditional NTRU key encapsulation mechanisms still suffer from poor computational efficiency, inability to compress ciphertexts, and a narrow range of secret values. To address these challenges, an optimization of NTRU-Prime–FPTRU (Fast Prime NTRU) constructed on LPPNF (large-Galois-group prime-degree prime-ideal number field) is presented. It provides enhanced security assurances and support for lossy compression of ciphertexts. Pseudo-Mersenne reduction and pseudo-Mersenne incomplete NTT are used to accelerate polynomial multiplication in LPPNF. Considering the situation of batch key generation in practical applications, we apply Montgomery inversion to key generation of FPTRU and explore the optimal batch size. With a batch size of 32, FPTRU-761 achieves a 4.7 \(\times \) efficiency improvement over serial key generation and an 80.7 \(\times \) improvement over SNTRU-Prime-761 batch key generation. FPTRU-653 matches the classical and quantum security of SNTRU-Prime-761. Integrated into OpenSSL, FPTRU-653 outperforms SNTRU-Prime-761 in various network conditions. For example, with 15.458 ms latency and \(15\%\) packet loss, FPTRU-653 completes 1.2 \(\times \) more handshakes than SNTRU-Prime-761.