A Flexible NTT-Based Multiplier for Post-Quantum Cryptography

Polynomial multiplication stands out as a highly demanding arithmetic process in the development of post-quantum cryptosystems. The importance of the number-theoretic transform (NTT) extends beyond post-quantum cryptosystems, proving valuable in enhancing existing security protocols such as digital signature schemes and hash functions. CRYSTALS-KYBER stands out as the sole public key encryption (PKE) algorithm chosen by the National Institute of Standards and Technology (NIST) in its third round selection, making it highly regarded as a leading post-quantum cryptography (PQC) solution. Faults have the potential to disrupt cryptographic systems, compromise data integrity, and enable side-channel attacks, making the incorporation of robust error detection mechanisms essential. This article introduces algorithm-level fault detection schemes in the NTT multiplication using Negative Wrapped Convolution ( NWC ) and the NTT tailored for Kyber Round 3, representing a significant enhancement compared with previous research. We evaluate this through the simulation of a fault model, ensuring that the conducted assessments accurately mirror the obtained results. Our fault detection scheme is designed to address both malicious fault injection attacks on Kyber and naturally occurring faults. Furthermore, we assessed the effectiveness of the proposed error detection scheme for the NTT implemented in both NWC and Kyber , using AMD/Xilinx Artix-7 FPGA, HLS and processor-based approaches. In our FPGA implementation of NWC , the integration of our error detection approach achieves near-100% fault coverage with minimal area overhead and results in only a 12% increase in latency compared with the original hardware design. Finally, we attained an error detection ratio of nearly 100% for the NTT operation in Kyber , with a clock cycle overhead of 16% on the Cortex-A72 processor.

<p>The national institute of standards and technology (NIST) has presented its draft of the module-lattice-based key-encapsulation mechanism standard (MLBKEMS), choosing cryptographic suite for algebraic lattices (CRYSTALS)- Kyber as the base encryption. Existing hardware implementations of modern cryptography will need to process the new standard efficiently. The primary process in CRYSTALS-Kyber key-encapsulation mechanism (KEM) is the number theoretic transform (NTT), which requires heavy computing power. This paper contributes an efficient hardware accelerator for NTT and inverse NTT (INTT) by CRYSTAL-Kyber parameters. The proposed design utilizes the K-RED algorithm for reducing polynomial multiplication. It also incorporates the BrentKung method for efficient modular addition and subtraction operation with an address generator to control the sequences of computation. On the Xilinx Artix 7 field programmable gate array (FPGA), our design achieves 262 MHz clock speed, utilizing only 1405 LUTs.</p>

Lattice-based cryptography is a novel approach to public key cryptography (PKC), of which the mathematical investigation (so far) resists attacks from quantum computers. By choosing a module learning with errors (MLWE) algorithm as the next standard, the National Institute of Standards and Technology (NIST) follows this approach. The multiplication of polynomials is the central bottleneck in the computation of lattice-based cryptography. Because PKC is mostly used to establish common secret keys, the focus is on compact area, power, and energy budget and, to a lesser extent, on throughput or latency. While most other work focuses on optimizing number theoretic transform (NTT)-based multiplications, in this article, we highly optimize a Toom–Cook-based multiplier. We demonstrate that a memory-efficient striding Toom–Cook with lazy interpolation results in a highly compact, low-power implementation, which, on top, enables a very regular memory access scheme. To demonstrate the efficiency, we integrate this multiplier into a Saber post-quantum accelerator, one of the four NIST finalists. Algorithmic innovation to reduce active memory, timely clock gating, and shift-add multiplier has helped to achieve 38% less power than state-of-the-art post-quantum cryptography (PQC) core, 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> less memory, 36.8% reduction in multiplier energy, and 118 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> reduction in active power with respect to state-of-the-art Saber accelerator (not silicon verified). This accelerator consumes 0.158- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {mm}^{2}$ </tex-math></inline-formula> active area, which is the lowest reported to date despite the process disadvantages of the state-of-the-art designs.

The emergence of large-scale quantum computing presents an imminent threat to contemporary public-key cryptosystems, with quantum algorithms such as Shor’s algorithm capable of efficiently breaking RSA and elliptic curve cryptography (ECC). This vulnerability has catalyzed accelerated standardization efforts for post-quantum cryptography (PQC) by the U.S. National Institute of Standards and Technology (NIST) and global security stakeholders. While theoretical security analysis of these quantum-resistant algorithms has advanced considerably, comprehensive real-world performance benchmarks spanning diverse computing environments—from high-performance cloud infrastructure to severely resource-constrained IoT devices—remain insufficient for informed deployment planning. This paper presents the most extensive cross-platform empirical evaluation to date of NIST-selected PQC algorithms, including CRYSTALS-Kyber and NTRU for key encapsulation mechanisms (KEMs), alongside BIKE as a code-based alternative, and CRYSTALS-Dilithium and Falcon for digital signatures. Our systematic benchmarking framework measures computational latency, memory utilization, key sizes, and protocol overhead across multiple security levels (NIST Levels 1, 3, and 5) in three distinct hardware environments and various network conditions. Results demonstrate that contemporary server architectures can implement these algorithms with negligible performance impact (&lt;5% additional latency), making immediate adoption feasible for cloud services. In contrast, resource-constrained devices experience more significant overhead, with computational demands varying by up to 12× between algorithms at equivalent security levels, highlighting the importance of algorithm selection for edge deployments. Beyond standalone algorithm performance, we analyze integration challenges within existing security protocols, revealing that naive implementation of PQC in TLS 1.3 can increase handshake size by up to 7× compared to classical approaches. To address this, we propose and evaluate three optimization strategies that reduce bandwidth requirements by 40–60% without compromising security guarantees. Our investigation further encompasses memory-constrained implementation techniques, side-channel resistance measures, and hybrid classical-quantum approaches for transitional deployments. Based on these comprehensive findings, we present a risk-based migration framework and algorithm selection guidelines tailored to specific use cases, including financial transactions, secure firmware updates, vehicle-to-infrastructure communications, and IoT fleet management. This practical roadmap enables organizations to strategically prioritize systems for quantum-resistant upgrades based on data sensitivity, resource constraints, and technical feasibility. Our results conclusively demonstrate that PQC is deployment-ready for most applications, provided that implementations are carefully optimized for the specific performance characteristics and security requirements of target environments. We also identify several remaining research challenges for the community, including further optimization for ultra-constrained devices, standardization of hybrid schemes, and hardware acceleration opportunities.

Information security is a fundamental and urgent issue in the digital transformation era. Cryptographic techniques and digital signatures have been applied to protect and authenticate relevant information. However, with the advent of quantum computers and quantum algorithms, classical cryptographic techniques have been in danger of collapsing because quantum computers can solve complex problems in polynomial time. Stemming from that risk, researchers worldwide have stepped up research on post-quantum algorithms to resist attack by quantum computers. In this review paper, we survey studies in recent years on post-quantum cryptography (PQC) and provide statistics on the number and content of publications, including a literature overview, detailed explanations of the most common methods so far, current implementation status, implementation comparisons, and discussion on future work. These studies focused on essential public cryptography techniques and digital signature schemes, and the US National Institute of Standards and Technology (NIST) launched a competition to select the best candidate for the expected standard. Recent studies have practically implemented the public key encryption/key encapsulation mechanism (PKE/KEM) and digital signature schemes on different hardware platforms and applied various optimization measures based on other criteria. Along with the increasing number of scientific publications, the recent trend of PQC research is increasingly evident and is the general trend in the cryptography industry. The movement opens up a promising avenue for researchers in public key cryptography and digital signatures, especially on algorithms selected by NIST.

Advances in quantum computers may pose a significant threat to existing public-key encryption methods, which are crucial to the current infrastructure of cyber security. Both RSA and ECDSA, the two most widely used security algorithms today, may be (in principle) solved by the Shor algorithm in polynomial time due to its ability to efficiently solve the discrete logarithm problem, potentially making present infrastructures insecure against a quantum attack. The National Institute of Standards and Technology (NIST) reacted with the post-quantum cryptography (PQC) standardization process to develop and optimize a series of post-quantum algorithms (PQAs) based on difficult mathematical problems that are not susceptible to being solved by Shor’s algorithm. Whilst high-powered computers can run these PQAs efficiently, further work is needed to investigate and benchmark the performance of these algorithms on lower-powered (constrained) devices and the ease with which they may be integrated into existing protocols such as TLS. This paper provides quantitative benchmark and handshake performance data for the most recently selected PQAs from NIST, tested on a Raspberry Pi 4 device to simulate today’s IoT (Internet of Things) devices, and provides quantitative comparisons with previous benchmarking data on a range of constrained systems. CRYSTALS-Kyber and CRYSTALS-Dilithium are shown to be the most efficient PQAs in the key encapsulation and signature algorithms, respectively, with Falcon providing the optimal TLS handshake size.

Standards provide critical benefits across a wide variety of contexts, including safety and health, environmental protection, and quality of products and services. However, while these benefits are generally acknowledged, estimating the social and economic value of standards and determining how specific entities and activities influence their development require careful analysis. In October of 2018, the National Institute of Standards and Technology (NIST) asked the RAND Corporation to estimate the benefit of NIST’s research contributing to particular fire safety standards. The original objectives of the project were to (1) document the role of the NIST in the standards development process, (2) estimate the value these standards provide to society, and (3) thereby inform the economic value of NIST’s contribution to these standards. This report presents results for the first two objectives. Given that NIST’s contribution is one of several inputs combining to create these standards, NIST’s share of the credit for their value could not be quantified. Our analysis focused on case studies in standards for home smoke alarms and for protecting structures at the wildland-urban interface (WUI). Our analysis draws on a wide variety of qualitative and quantitative methods to holistically describe the impacts of these standards and NIST’s role in their development. The intended audience of this report includes those who work on fire safety research, fire safety standards, building codes, and technology transfer. The conclusions presented here may also be of interest for broader resource allocation and federal budget justification purposes. Finally, this report was written to be accessible to any interested members of the general public.

The growth of quantum computing reveals a series of significant threats to cryptographic systems known today, such as RSA, ECC, and Diffie-Hellman, which are extremely important for Internet security, but are threatened by the increase in possible quantum attacks. The area of public and private key cryptography is vast. Therefore, this article addresses post-quantum cryptography (PQC) algorithms and the challenges of implementing them in Internet of Things (IoT) devices, given the difficulty of application due to restricted resources, such as RAM and clock speed . To this end, we will discuss the need for standardization of algorithms considering low-resource IoT devices, prioritizing RAM over ROM, meeting the needs of low-memory devices, which are lighter. The National Institute of Standards and Technology (NIST) has validated four cryptographic systems that are secure against quantum attacks. We analyze the implications of these systems on the infrastructure of current networks and will compare in detail these algorithms and their respective strengths, weaknesses, and trade-offs. We evaluate the feasibility of post-quantum encryption (PQC) algorithms in resource-constrained IoT devices using the ESP-WROOM-32 microcontroller. Three cryptographic schemes were implemented and compared.

The Clean Air Mercury Rule (CAMR) which was published in the Federal Register on May 18, 2005, requires that calibration of mercury continuous emissions monitors (CEMs) be performed with NIST-traceable standards. Western Research Institute (WRI) is working closely with the Electric Power Research Institute (EPRI), the National Institute of Standards and Technology (NIST), and the Environmental Protection Agency (EPA) to facilitate the development of the experimental criteria for a NIST traceability protocol for dynamic elemental mercury vapor generators. The traceability protocol will be written by EPA. Traceability will be based on the actual analysis of the output of each calibration unit at several concentration levels ranging from about 2-40 ug/m{sup 3}, and this analysis will be directly traceable to analyses by NIST using isotope dilution inductively coupled plasma/mass spectrometry (ID ICP/MS) through a chain of analyses linking the calibration unit in the power plant to the NIST ID ICP/MS. Prior to this project, NIST did not provide a recommended mercury vapor pressure equation or list mercury vapor pressure in its vapor pressure database. The NIST Physical and Chemical Properties Division in Boulder, Colorado was subcontracted under this project to study the issue in detail and to recommend a mercury vapormore » pressure equation that the vendors of mercury vapor pressure calibration units can use to calculate the elemental mercury vapor concentration in an equilibrium chamber at a particular temperature. As part of this study, a preliminary evaluation of calibration units from five vendors was made. The work was performed by NIST in Gaithersburg, MD and Joe Rovani from WRI who traveled to NIST as a Visiting Scientist.« less

The rapid advancement in quantum technology has initiated a new round of post-quantum cryptography (PQC) related exploration. The key encapsulation mechanism (KEM) Saber is an important module lattice-based PQC, which has been selected as one of the PQC finalists in the ongoing National Institute of Standards and Technology (NIST) standardization process. On the other hand, however, efficient hardware implementation of KEM Saber has not been well covered in the literature. In this paper, therefore, we propose a novel cyclic-row oriented processing (CROP) strategy for efficient implementation of the key arithmetic operation of KEM Saber, i.e., the polynomial multiplication. The proposed work consists of three layers of interdependent efforts: (i) first of all, we have formulated the main operation of KEM Saber into desired mathematical forms to be further developed into CROP based algorithms, i.e., the basic version and the advanced higher-speed version; (ii) then, we have followed the proposed CROP strategy to innovatively transfer the derived two algorithms into desired polynomial multiplication structures with the help of a series of algorithm-architecture co-implementation techniques; (iii) finally, detailed complexity analysis and implementation results have shown that the proposed polynomial multiplication structures have better area-time complexities than the state-of-the-art solutions. Specifically, the field-programmable gate array (FPGA) implementation results show that the proposed design, e.g., the basic version has at least less 11.2% area-delay product (ADP) than the best competing one (Cyclone V device). The proposed high-performance polynomial multipliers offer not only efficient operation for output results delivery but also possess low-complexity feature brought by CROP strategy. The outcome of this work is expected to provide useful references for further development and standardization process of KEM Saber.

A Look at its Past Decade and a Gaze towards its Future. As the National Metrology Institute (NMI) for the United States, the National Institute of Standards and Technology (NIST), formerly the National Bureau of Standards, has provided measurement services, both calibrations and reference materials, for more than 100 years. Through these services, our customers have benefitted from our measurement capabilities and expertise in many areas, including amount of substance; dimensional metrology; electricity and magnetism; ionizing radiation; mass and related quantities; photometry and radiometry; thermodynamics; and time and frequency. NIST’s customers have also had access to some of the lowest measurement uncertainties available and a dependable way to establish traceability to the International System of Units (SI) [http://www.nist.gov/pml/wmd/metric/si-units.cfm].In response to the signing of the International Committee for Weights and Measures (CIPM) Mutual Recognition Arrangement (MRA), NIST first established an institution-wide quality system for the measurement services 10 years ago [http://www.bipm.org/en/cipm-mra/objectives.html]. NIST’s Quality System for Measurement Services has advanced the quality of service and measurements we provide our customers by fostering an environment in which NIST management and staff work towards continual improvement in the development and delivery of NIST measurement services. This paper describes NIST’s Quality System for the Measurement Services and its relevance to international standards of quality, such as the International Organization for Standardization and the International Electrotechnical Commission (ISO/IEC) 17025 standard and ISO Guide 34 [http://www.nist.gov/nistqs/]. It also provides a history of this quality system and a glimpse of future goals for improving its implementation.

As cybersecurity issues surge, it highlights the pressing need for increased awareness. In our digitally interconnected world, where information technology underpins the lives of individuals, businesses, and even national security, the threat of cyberattacks looms large. To enhance national cybersecurity preparedness, there is a critical call to action: we must promote public awareness of cybersecurity issues and bolster the ranks of trained cybersecurity professionals. This research introduces a novel cybersecurity awareness model based on the National Institute of Standards and Technology (NIST). Its primary goal is to make NIST accessible to secondary school students pursuing ICT courses and their invaluable resource, the school counselling units. The model aims to instil cybersecurity awareness in secondary school students and guide them in choosing the most suitable higher education paths, particularly in the ICT and cybersecurity fields. The study comprises three phases. In the first phase, a systematic literature review (SLR) examines globally applicable cybersecurity education models. The second phase investigates the implementation of cybersecurity education for secondary school students in Malaysia. This includes interviews with school counselling units responsible for guiding students toward higher education and surveys of students in grades four and five enrolled in ICT courses. The third and pivotal phase focuses on developing the proposed model. It involves analysing and implementing the results of the SLR, mapping them to the NIST framework, and incorporating themes from interviews and surveys. As a tangible representation of the model, a mobile application prototype has been developed. The Cybersecurity Awareness Model empowers school counselling units to seamlessly integrate career exploration with career decision-making for secondary students at any stage of their development. Moreover, it offers a means to create strategies for after-school programs, particularly in the dynamic field of cybersecurity. This model is expected to guide students in exploring academic majors and careers, preparing for higher education post-high school, initiating internships or job searches, and adapting to a world in constant flux. In doing so, it not only empowers individuals but also strengthens the nation's resilience in the face of cybersecurity challenges.

In the fall of 2019, the National Institute of Standards and Technology (NIST) funded threes studies to better understand equity and inclusivity. This report documents phase two of a three phased sequential, exploratory mixed methods study designed to provide an in-depth look at the population of NIST federal employees to identify factors, attitudes, and processes that might result in gender- specific barriers at NIST. Phase 1 analyzed human resources demographic data, compensation data, and performance data of NIST federal employees from 2011 to 2019 to determine any relevant trends. Phase 1 informed the development of an in-depth interview protocol designed to identify the differences, if any, in the ways in which men and women experience work at NIST. A total of 40 (36 female and 4 male) participants were interviewed. Three interconnected themes emerged in the data: 1) a culture at NIST that creates a Chilly Climate for women; 2) gendered experiences that contribute to and are outcomes of that chilly climate; and 3) gendered outcomes that influence women s experiences in the organization. The culture has evolved from NIST s scientific roots, scientific excellence, a strong belief in meritocracy, and as a Federal agency. Each of these characteristics contribute to a gendered social structure and the perception that change is not needed. This backdrop sets the stage for the characterizations of NIST from the interviews as a Boys Club and an Elitist environment. The radically different perspectives of men and women based in the culture result in experiences and outcomes that provide advantages and opportunities for men while erecting barriers to survival for women, including isolation and possibly exclusion. These barriers result in consequences of discrimination as well as lack of trust and resignation. Participant quotes are used as exemplars to provide details related to each of these themes. Overall, the interviews demonstrate that women and men experience a very different NIST.

The National Institute of Standards and Technology (NIST), formerly the National Bureau of Standards, was established by the U.S. Congress in 1901 and charged with establishing a measurement foundation to facilitate U.S. and international commerce. NIST provides reference materials and reference instruments that are used to ensure the accuracy, metrological traceability, and comparability of measurement results in many diverse fields of science, industry, and technology. This document provides and explains the vocabulary used at NIST to describe the reference materials and reference instruments available to NIST s customers. This document also describes the methods used in developing NIST reference materials. The definitions and descriptions provided supersede those used in the original versions of this publication, NIST SP260-136 and SP260-136-2020.

This paper presents a summary of the strategies and activities underway at the National Institute of Standards and Technology (NIST) in electronics packaging, interconnection and assembly (P/I/A). In addition, a sampling of collaborations involving these works is included. The overall NIST effort in P/I/A is composed of targeted programs conducted by the NIST laboratories and by the NIST Advanced Technology Program (ATP). A dominant aspect of the laboratory-based P/I/A program focuses on the metrology and data needed to support the product technologies envisioned within industry roadmaps. A significant aspect of the work includes efforts in metrology, materials, complex material assemblies, and microelectronic components and circuits. In parallel, the NIST ATP is supporting on a cost-share basis a variety of industry-based development projects of high-risk enabling technologies for new or improved products, manufacturing, and processes in P/I/A.