The rise of quantum computing necessitates post-quantum cryptography (PQC) to secure Internet communications on edge platforms. CTRU is an NTRU-based key encapsulation mechanism (KEM) that features a small modulus and an efficient scaledE8lattice encoding, offering strong security and performance. However, two critical gaps impede its deployment for Internet of Things (IoT) edge platforms: the absence of an optimized implementation for ARMv8 devices, which dominate the mobile and embedded IoT ecosystems, and a lack of integration and evaluation in practical protocols such as Transport Layer Security (TLS) 1.3. To address these challenges, we present the first NEON-optimized CTRU implementation for ARMv8-A. Our implementation reduces CPU cycles by 3.24×, 2.62×, and 2.99× in key generation (KeyGen), encapsulation (Encaps), and decapsulation (Decaps) compared to the reference C (REF-C) implementation, while lowering energy consumption by 55.2%. Among all evaluated KEMs, it achieves the lowest energy consumption and a competitive memory footprint. We further design a batch key generation scheme that boosts KeyGen throughput by 3.73×. Finally, we integrate CTRU into TLS 1.3 to enable post-quantum (PQ) key exchange. Comprehensive benchmarks show that CTRU outperforms all evaluated KEMs and classical key exchange scheme Elliptic Curve Diffie-Hellman Secp384r1 (ECDH P384) on ARMv8-A platform. Specifically, it achieves lower TLS handshake latency and higher throughput under ideal network conditions, and its handshake latency distribution is superior to that of all alternatives under Narrow Band IoT (NB-IoT) constraints. These results demonstrate CTRU’s practical suitability for real-world deployment on IoT edge platforms.

In 1994, Shor’s algorithm was introduced, which exploits the capabilities of quantum computers (QCs) to solve integer factorization and discrete logarithm problems, posing a significant threat to traditional public-key cryptosystems based on these problems. The widely used Internet security protocol, TLS, relies on ECC as one of its cryptographic primitives. As quantum computing continues to advance, there is an urgent need to replace the cryptographic primitives used in TLS with post-quantum cryptographic (PQC) algorithms that can resist quantum attacks. Given the proliferation of IoT devices, the security of IoT embedded systems has become a critical concern. In this article, we present an optimized implementation of PQC algorithms on IoT embedded devices, introducing the first implementation of the NTTRU key encapsulation mechanism (KEM) based on the ARMv8 architecture. ARMv8 is the dominant processor architecture in current mobile phones and tablets. By utilizing the NEON engine of the ARMv8 architecture, we have accelerated the performance bottlenecks in the NTTRU algorithm, achieving an overall speedup of 2.85 to 3.27 times. Moreover, we propose a detailed design and implementation of a hybrid migration of NTTRU KEM into TLS 1.3 on embedded platforms, and we perform experimental and comparative analysis of the TLS 1.3 handshake performance with other standardized KEMs. Our experimental results demonstrate that the hybrid migration of our NEON-optimized NTTRU implementation significantly enhances TLS handshake performance compared to its C implementation, while also outperforming other PQC KEMs.

CRYSTALS-Dilithium is a lattice-based signature scheme that is being standardized by NIST as the primary post-quantum signature algorithm. In this work, we present a comprehensive study of optimizing the implementation of Dilithium using Advanced Vector Extensions (AVX), specifically AVX2 and the latest AVX-512. We begin by introducing an enhanced parallel small polynomial multiplication with tailored early evaluation (PSPM-TEE) to accelerate the signing process. We provide both AVX2 and AVX-512 implementations of PSPM-TEE, demonstrating that our PSPM algorithm outperforms the traditional NTT by 47%-66% on these platforms. Next, we propose a tailored reduction method that is simpler and faster than Montgomery reduction. By leveraging AVX-512IFMA, we further minimize the CPU cycles required for the tailored reduction. Finally, we present a fully vectorized implementation of Dilithium using AVX-512, carefully optimizing most of the Dilithium functions to improve both time and space efficiency simultaneously. As a result of these optimizations, our AVX-512 implementation achieves performance improvements of 2.25×/2.07×/2.20× in key generation, 2.07×/2.13×/2.36× in signing, and 2.20×/2.36×/2.46× in verification for the Dilithium2/3/5 parameter sets, respectively compared to the state-of-the-art AVX2 implementation.

To tackle the challenges introduced by quantum computers to traditional public key cryptography, the domain of post-quantum cryptography (PQC) has taken center stage. Within this domain, the evaluation of computational performance emerges as a pivotal yardstick. Notably, NTTRU stands for one of the most efficient PQC schemes for key encapsulation mechanisms (KEM). This paper introduces the first optimized implementation of NTTRU on ARMv8 architecture. By leveraging the capabilities of the NEON engine, we strategically optimize the core modules of NTTRU: NTT/INTT, polynomial base case multiplication, and polynomial inversion. These optimizations have resulted in remarkable performance gains of 7.37×, 6.10×, 5.91×, and 4.43×, respectively when compared to the reference implementation. For the whole implementation, we achieve performance improvement of 2.85×, 2.36×, and 3.27× in key generation, encapsulation, and decapsulation respectively.

The lattice-based signature scheme CRYSTALS-Dilithium is one of the two signature finalists in the third round NIST post-quantum cryptography (PQC) standardization project. For applications of low-power Internet-of-Things (IoT) devices, recent research efforts have been focusing on the performance optimization of PQC algorithms on embedded systems. In particular, performance optimization is more demanding for PQC signature algorithms that are usually significantly more time-consuming than PQC public-key encryption counterparts. For most cryptographic algorithms based on algebraic lattices including Dilithium, the fundamental and most time-consuming operation is polynomial multiplication over rings. For this computational task, number theoretic transform (NTT) is the most efficient multiplication method for NTT-friendly rings, and is now the typical technique for performing fast polynomial multiplications when implementing lattice-based PQC algorithms.

The one‐dimensional (2D) chaotic encryption algorithm has good encryption performance. For its properties, such as the excellent complexity, pseudo‐randomness, and sensitivity to the initial value of the chaotic sequence. However, compared with other methods, its biggest drawback is that the key space is too small. To address these problems, in this study, the authors introduce an improved 2D logistic sine chaotic map (2D‐LSMM). A novel image encryption scheme based on dynamic DNA sequences encryption and improved 2D‐LSMM is presented. The logistic map is used to control the input of the sine map. And the encoding and operation rules of DNA sequences are determined by 2D‐LSMM chaotic sequences. By implementing dynamic DNA sequence encryption, the encryption process becomes more complicated and harder to be attacked. Simulation experimental results and security analysis show that the authors’ encryption scheme not only achieves proper encryption but can also resist different attacks.