Abstract We present a probabilistic modeling framework for quantifying decryption-failure probability (DFP) in CRYSTALS–Kyber , the lattice-based key encapsulation mechanism standardized by National Institute of Standards and Technology as module-lattice-based key-encapsulation mechanism. Our method combines exact tail computation of Kyber’s centered-binomial noise distribution using FFT-based convolution with principled comparisons to classical concentration inequalities such as Hoeffding and Bernstein. This hybrid analytical-computational approach yields implementation-independent upper bounds on DFP that are exponentially small in the security parameter. Specifically, we compute two-sided tails for aggregated noise variables, translate those into per-ciphertext failure probabilities through a transparent union bound, and determine the minimal reconciliation margins required to ensure DFP ⩽ 2 − λ for λ ∈ { 128 , 192 , 256 } . Across Kyber-like parameter regimes, Bernstein-type inequalities consistently overestimate risk compared to the exact probabilistic tails, which are several orders of magnitude smaller. The resulting gap highlights the conservatism of inequality-based analyses and clarifies the quantitative safety margins inherent to Kyber’s design. These findings contribute to the broader effort of modeling reliability in post-quantum cryptographic primitives using probabilistic and computational methodologies.
Abstract We present a probabilistic modeling framework for quantifying decryption-failure probability (DFP) in CRYSTALS–Kyber , the lattice-based key encapsulation mechanism standardized by National Institute of Standards and Technology as module-lattice-based key-encapsulation mechanism. Our method combines exact tail computation of Kyber’s centered-binomial noise distribution using FFT-based convolution with principled comparisons to classical concentration inequalities such as Hoeffding and Bernstein. This hybrid analytical-computational approach yields implementation-independent upper bounds on DFP that are exponentially small in the security parameter. Specifically, we compute two-sided tails for aggregated noise variables, translate those into per-ciphertext failure probabilities through a transparent union bound, and determine the minimal reconciliation margins required to ensure DFP ⩽ 2 − λ for λ ∈ { 128 , 192 , 256 } . Across Kyber-like parameter regimes, Bernstein-type inequalities consistently overestimate risk compared to the exact probabilistic tails, which are several orders of magnitude smaller. The resulting gap highlights the conservatism of inequality-based analyses and clarifies the quantitative safety margins inherent to Kyber’s design. These findings contribute to the broader effort of modeling reliability in post-quantum cryptographic primitives using probabilistic and computational methodologies.
Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digitalsignature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of postquantum security.
Abstract Quantum computing poses a significant threat to the security of many current cryptographic algorithms. This imminent risk has accelerated the development and standardization of new cryptosystems, known as post-quantum cryptosystems and designed to protect digital information in the quantum era using classical computing resources. CRYSTALS-Kyber is a lattice-based post-quantum encryption scheme that has been selected as a standard by the National Institute of Standards and Technology. This work presents a novel kleptographic attack against the CRYSTALS-Kyber scheme, providing both theoretical insights and practical results that demonstrate its feasibility. One of the conclusions is that this post-quantum cryptosystem may be vulnerable to kleptographic backdoors. As a result, this study offers a mathematical analysis along with software implementations and practical methodologies to detect such backdoors, thereby contributing to the development of more transparent and verifiable cryptographic standards.
As the advent of quantum computing threatens traditional cryptographic protocols, hybrid classical-quantum secure communication infrastructures have emerged as a critical frontier in cybersecurity. This paper explores the integration of post-quantum cryptographic algorithms—specifically CRYSTALS-Kyber for key encapsulation and CRYSTALS-Dilithium for digital signatures—into hybrid communication architectures designed to resist quantum-level attacks. Leveraging lattice-based cryptographic primitives, both algorithms have been selected for standardization by NIST due to their robust security and performance characteristics. This study evaluates their implementation in real-world communication stacks, assesses latency and throughput under hybrid channel configurations, and proposes a layered security architecture combining classical and quantum-resilient mechanisms. Furthermore, it examines key management, digital trust, and infrastructure scalability in a post-quantum context. Simulation results and hardware-based validations are used to determine practical deployment feasibility in critical sectors such as finance, defense, and healthcare. The findings offer a comprehensive framework for securing data in transitional computing eras, ensuring forward secrecy, and maintaining operational integrity against future adversarial quantum threats.
The emergence of quantum computing poses an existential threat to classical cryptographic systems that form the backbone of contemporary digital security infrastructure. RSA, the most widely deployed public-key cryptosystem, relies on the computational hardness of integer factorization, a problem efficiently solvable by quantum computers using Shor's algorithm. This impending vulnerability has catalyzed the development of post-quantum cryptographic alternatives designed to withstand both classical and quantum attacks. CRYSTALS-Kyber, standardized by NIST as ML-KEM, represents the forefront of latticebased key encapsulation mechanisms, offering quantum resistance through the Module Learning With Errors (MLWE) problem. This paper presents a comprehensive comparative analysis of RSA and Kyber, examining their mathematical foundations, security architectures, operational characteristics, and performance metrics across diverse computational environments. The study investigates the fundamental trade-offs between legacy systems optimized for classical threat models and emerging quantum-resistant algorithms designed for future-proof security. Through detailed analysis of key generation, encryption/encapsulation, decryption/decapsulation operations, and security guarantees, this research establishes the technical rationale behind NIST's selection of Kyber as the primary post-quantum key establishment mechanism. The findings demonstrate that while RSA maintains advantages in key size efficiency, Kyber's superior performance profile, quantum resilience, and robust security foundation position it as the essential successor for securing digital communications in the quantum era. This comprehensive study provides critical insights for organizations transitioning from classical to post-quantum cryptographic infrastructure
The rapid expansion of 5G wireless networks has introduced unprecedented security challenges, particularly in the face of emerging quantum computing threats. Traditional cryptographic schemes, including Elliptic Curve Cryptography (ECC), face vulnerabilities against quantum-based attacks, necessitating a transition toward quantum-resistant security solutions. A hybrid cryptographic framework incorporating CRYSTALS-Kyber for key encapsulation is proposed to mitigate these threats. CRYSTALS-Kyber, a lattice-based post-quantum cryptographic algorithm, enhances key exchange mechanisms by resisting quantum decryption attempts while maintaining computational efficiency. The proposed framework integrates CRYSTALS-Kyber with conventional ECC to establish a dual-layer security model that ensures backward compatibility while progressively adapting to quantum security standards. Simulation results demonstrate that the hybrid approach significantly enhances key exchange security while maintaining a low computational overhead. In particular, latency is reduced by 18.4% compared to standalone ECC-based key exchange, while key generation time improves by 22.7% due to CRYSTALS-Kyber’s efficient polynomial arithmetic operations. Furthermore, encryption throughput increases by 31.2%, demonstrating the model''s capability to secure high-speed 5G transmissions with minimal performance trade-offs.
Module Learning with Errors (M-LWE) based key reconciliation mechanisms (KRM) can be viewed as quantizing an M-LWE sample according to a lattice codebook. This paper describes a generic M-LWE-based KRM framework, valid for any dimensional lattices and any modulusqwithout a dither. Our main result is an explicit upper bound on the decryption failure rate (DFR) of M-LWE-based KRM. This bound allows us to construct optimal lattice quantizers to reduce the DFR and communication cost simultaneously. Moreover, we present a KRM scheme using the same security parameters(q,k,η1,η2)as in Kyber. Compared with Kyber, the communication cost is reduced by up to 36.47% and the DFR is reduced by a factor of up to 299. The security arguments remain the same as Kyber.