Following the completion of the NIST post-quantum cryptography standardization, Kyber has been adopted as a key encapsulation mechanism (KEM) for quantum-resistant communication. Although lattice-based KEMs provide strong security and efficiency, most existing designs restrict the cyclotomic ring dimension to powers of two, which limits parameter flexibility for heterogeneous and resource-constrained Internet of Things (IoT) devices. In this paper, we propose Fyber, a post-quantum KEM based on the Module Learning With Errors (M-LWE) problem over a module ring defined by the cyclotomic polynomial f(x)=xn−xn/2+1, where n is a product of powers of 2 and 3. This construction enables mixed-radix parameter selection and allows finer-grained trade-offs between security and efficiency. To further improve performance on constrained platforms, we introduce an efficient non-Gaussian sampling method. The proposed KEM supports flexible security-level stratification for IoT applications, achieving reduced public key and ciphertext sizes for selected parameter sets at the cost of moderately increased computational overhead compared to Kyber, and fills intermediate security gaps between existing standardized parameter sets.
Following the completion of the NIST post-quantum cryptography standardization, Kyber has been adopted as a key encapsulation mechanism (KEM) for quantum-resistant communication. Although lattice-based KEMs provide strong security and efficiency, most existing designs restrict the cyclotomic ring dimension to powers of two, which limits parameter flexibility for heterogeneous and resource-constrained Internet of Things (IoT) devices. In this paper, we propose Fyber, a post-quantum KEM based on the Module Learning With Errors (M-LWE) problem over a module ring defined by the cyclotomic polynomial f(x)=xn−xn/2+1, where n is a product of powers of 2 and 3. This construction enables mixed-radix parameter selection and allows finer-grained trade-offs between security and efficiency. To further improve performance on constrained platforms, we introduce an efficient non-Gaussian sampling method. The proposed KEM supports flexible security-level stratification for IoT applications, achieving reduced public key and ciphertext sizes for selected parameter sets at the cost of moderately increased computational overhead compared to Kyber, and fills intermediate security gaps between existing standardized parameter sets.
In order to resist the security risks caused by quantum computing, post-quantum cryptography (PQC) has been a research focus. Constructing a key encapsulation mechanism (KEM) based on lattices is one of the promising PQC routines. The algebraically structured learning with errors (LWE) problem over power-of-two cyclotomics has been one of the most widely used hardness assumptions for lattice-based cryptographic schemes. However, power-of-two cyclotomic rings may be exploited in the inflexibility of selecting parameters. Recently, trinomial cyclotomic rings of the form Zq[x]/(xn−xn/2+1), where n=2k3l, k≥1,l≥0, have received widespread attention due to their flexible parameter selection. In this paper, we propose Tyber, a variant scheme of the NIST-standardized KEM candidate Kyber over trinomial cyclotomic rings. We provide three parameter sets, aiming at the quantum security of 128, 192, and 256 bits (actually achieving 129, 197, and 276 bits) with matching and negligible error probabilities. When compared to Kyber, our Tyber exhibits stronger quantum security, by 22, 31, and 44 bits, than Kyber for three security levels.
Resource-constrained devices such as wireless sensors and Internet of Things (IoT) devices have become ubiquitous in our digital ecosystem. These devices generate and handle a major part of our digital data. However, due to the impending threat of quantum computers on our existing public-key cryptographic schemes and the limited resources available on IoT devices, it is important to design lightweight post-quantum cryptographic (PQC) schemes suitable for these devices.In this work, we explored the design space of learning with error-based PQC schemes to design a lightweight key-encapsulation mechanism (KEM) suitable for resourceconstrained devices. We have done a scrupulous and extensive analysis and evaluation of different design elements, such as polynomial size, field modulus structure, reduction algorithm, and secret and error distribution of an LWE-based KEM. Our explorations led to the proposal of a lightweight PQC-KEM, Rudraksh, without compromising security. Our scheme provides security against chosen ciphertext attacks (CCA) with more than 100 bits of Core-SVP post-quantum security and belongs to the NIST-level-I security category (provide security at least as much as AES-128). We have also shown how ASCON can be used for lightweight pseudo-random number generation and hash function in the lattice-based KEMs instead of the widely used Keccak for lightweight design. Our FPGA results show that Rudraksh currently requires the least area among the PQC KEMs of similar security. Our implementation of Rudraksh provides a ~3x improvement in terms of the area requirement compared to the state-of-the-art areaoptimized implementation of Kyber, can operate at 63%-76% higher frequency with respect to high-throughput Kyber, and improves time-area-product ~2x compared to the state-of-the-art compact implementation of Kyber published in HPEC 2022.
Current improvements in quantum computing present a substantial challenge to classical cryptographic systems, which typically rely on problems that can be solved in polynomial time using quantum algorithms. Consequently, post-quantum cryptography (PQC) has emerged as a promising solution to emerging quantum-based cryptographic challenges. The greatest threat is public-key cryptosystems, which are primarily responsible for key exchanges. In PQC, key encapsulation mechanisms (KEMs) are crucial for securing key exchange protocols, particularly in Internet communication, virtual private networks (VPNs), and secure messaging applications. CRYSTALS-Kyber and NTRU are two well-known PQC KEMs offering robust security in the quantum world. However, even when quantum computers are functional, they are not easily accessible. IoT devices will not be able to utilize them directly, so there will still be a requirement to protect IoT devices from quantum attacks. Concerns such as limited computational power, energy efficiency, and memory constraints in devices such as those used in IoTs, embedded systems, and smart cards limit the use of these techniques in constrained environments. These concerns always arise there. To address this issue, this study conducts a broad comparative analysis of Kyber and NTRU, with special focus on their security, performance, and implementation efficiency in such environments (IOT/constrained environments). In addition, a case study was conducted by applying KEMs to a low-power embedded device to analyze their performance in real-world scenarios. These results offer an important comparison for cyber security engineers and cryptographers who are involved in integrating post-quantum cryptography into resource-constrained devices.
In the field of post-quantum cryptography, lattice-based cryptography has received the most noticeable attention. Most lattice-based cryptographic schemes are constructed based on the polynomial ring Rq= Zq[x]/f (x), using a cyclotomic polynomial f (x). Until now, the most preferred cyclotomic polynomials have been xn+ 1, where n is a power of two, and xn+ · · · + x + 1, where n + 1 is a prime. The former results in the smallest decryption error size, but the choice of degree is limited. On the other hand, the latter gives rise to the largest decryption error size, but the choice of degree is very flexible. In this paper, we use a new polynomial ring Rq = Zq/f (x) with a cyclotomic trinomial f (x) = xn- xn/2+ 1 as an intermediate that combines the advantages of the other rings. Since the degree n is chosen freely as n = 2a3bfor positive integers a and b, the choice of the degree n is moderate. Furthermore, since the error propagation is small in the middle of polynomial multiplication in the new ring, if the middle part is truncated and used, the decryption error size can be reduced. Based on these observations, we propose a new, practical key encapsulation mechanism (KEM) that is constructed over a ring with a cyclotomic trinomial. The security of our KEM is based on the hardness of ring learning-with-rounding (LWR) problems. With appropriate parameterization for the current 128-bit security model, we show that our KEM obtains shorter secret keys and ciphertexts, especially compared to the previous Ring-LWR-based KEM, Round5, with no error correction code. We then implement our KEM and compare its performance with that of several KEMs that were presented in the second round of the NIST PQC conference.
The rapid advancement of quantum computing poses significant threats to classical cryptographic methods, such as Rivest–Shamir–Adleman (RSA) and Elliptic Curve Cryptography (ECC), which currently secure Internet of Things (IoT) and cloud communications. Post-Quantum Cryptography (PQC), particularly lattice-based schemes, has emerged as a promising alternative. CRYSTALS-Kyber, standardized by the National Institute of Standards and Technology (NIST) as ML-KEM, has shown efficiency and practicality for constrained IoT devices. Most existing research has focused on PQC within the Transport Layer Security (TLS) protocol. Consequently, a critical gap exists in understanding PQC’s performance in lightweight IoT protocols. These are Message Queuing Telemetry Transport (MQTT) and Constrained Application Protocol (CoAP), particularly under adverse network conditions. To address this gap, this paper provides a systematic review of the literature on the network resilience and performance of CRYSTALS-Kyber when integrated into these protocols operating over lossy and high-latency networks. Additional challenges include non-standardized integration, resource limitations, and side-channel vulnerabilities. This review provides a structured synthesis of current knowledge, highlights unresolved trade-offs between security and efficiency, and outlines future research directions, including protocol-level optimization, lightweight signature schemes, and resilience testing of PQC-secured IoT protocols under realistic conditions.
Quantum computing poses a significant threat to Internet of Things (IoT) communications that rely on classical cryptographic algorithms such as RSA, Diffie–Hellman, and Elliptic Curve Cryptography (ECC). These algorithms are vulnerable to Shor’s algorithm, making long-term data security uncertain, particularly for IoT devices with extended operational lifespans. Post-quantum cryptographic (PQC) algorithms offer resistance to quantum attacks; however, their deployment on resource-constrained IoT devices remains challenging due to limitations in processing power, memory, and energy consumption. This study benchmarks seven Key Encapsulation Mechanisms (KEMs) ML-KEM, Kyber, NTRU, BIKE, Classic McEliece, FrodoKEM, and sntrup761 across key generation, encapsulation, and decapsulation operations. Experiments were conducted using the liboqs library in a virtualized Linux environment running WSL2 to simulate constrained computing conditions. Results revealed substantial performance differences among the algorithms. ML-KEM-512 achieved the best overall performance, completing all operations in under 14 µs, while Kyber-512 showed similar efficiency. NTRU provided the fastest encapsulation but incurred significantly higher key-generation costs. BIKE, FrodoKEM, and Classic McEliece exhibited execution times unsuitable for real-time IoT applications. Overall, lattice-based schemes, particularly ML-KEM and Kyber, emerged as the most practical PQC solutions for resource-constrained IoT environments. The findings also demonstrate the usefulness of virtualized benchmarking for deployment planning.