Post-quantum Cryptographic Algorithms Research Articles

The Future of Cybersecurity in the Age of Quantum Computers

The first week of August 2022 saw the world’s cryptographers grapple with the second shocker of the year. Another one of the four post-quantum cryptography (PQC) algorithms selected by the NIST (National Institute of Standards and Technology) in a rigorous 5-year process was cracked by a team from Belgium. They took just 62 min and a standard laptop to break the PQC algorithm to win a USD 50,000 bounty from Microsoft. The first shocker came 6 months earlier, when another of the NIST finalists (Rainbow) was taken down. Unfortunately, both failed PQC algorithms are commercially available to consumers. With 80 of the 82 PQC candidates failing the NIST standardization process, the future of the remaining two PQC algorithms is, at best, questionable, placing the rigorous 5-year NIST exercise to build a quantum-safe encryption standard in jeopardy. Meanwhile, there is no respite from the quantum threat that looms large. It is time we take a step back and review the etiology of the problem de novo. Although state-of-the-art computer security heavily relies on cryptography, it can indeed transcend beyond encryption. This paper analyzes an encryption-agnostic approach that can potentially render computers quantum-resistant. Zero-vulnerability computing (ZVC) secures computers by banning all third-party permissions, a root cause of most vulnerabilities. ZVC eliminates the complexities of the multi-layered architecture of legacy computers and builds a minimalist, compact solid-state software on a chip (3SoC) that is robust, energy-efficient, and potentially resistant to malware as well as quantum threats.

Post Quantum Design in SPDM for Device Authentication and Key Establishment

The Security Protocol and Data Model (SPDM) defines a set of flows whose purpose includes the authentication of a computing device’s hardware identity. SPDM also allows for the creation of a secure session wherein data communication between two devices has both confidentiality and integrity protection. The present version of SPDM, namely version 1.2, relies upon traditional asymmetric cryptographic algorithms, and these algorithms are known to be vulnerable to quantum attacks. This paper describes the means by which support for post-quantum (PQ) cryptography can be added to the SPDM protocol in order to prepare SPDM for the upcoming world of quantum computing. As part of this paper, we examine the SPDM 1.2 protocol and discuss various aspects of using PQC algorithms, including negotiation of the use of post-quantum cryptography (PQC) algorithms, support for device identity reporting, mechanisms for device authentication, and establishing a secure session. We consider so-called “hybrid modes” where both classical and PQC algorithms are used to achieve security properties, especially given the fact that these modes are important during the transition period from the classical to the quantum computing regime. We also share our experience with implementing a software embodiment of PQC in SPDM, namely “PQ-SPDM”, and we provide benchmarks that evaluate a subset of the winning NIST PQC algorithms.

Transitioning organizations to post-quantum cryptography.

Quantum computers are expected to break modern public key cryptography owing to Shor's algorithm. As a result, these cryptosystems need to be replaced by quantum-resistant algorithms, also known as post-quantum cryptography (PQC) algorithms. The PQC research field has flourished over the past two decades, leading to the creation of a large variety of algorithms that are expected to be resistant to quantum attacks. These PQC algorithms are being selected and standardized by several standardization bodies. However, even with the guidance from these important efforts, the danger is not gone: there are billions of old and new devices that need to transition to the PQC suite of algorithms, leading to a multidecade transition process that has to account for aspects such as security, algorithm performance, ease of secure implementation, compliance and more. Here we present an organizational perspective of the PQC transition. We discuss transition timelines, leading strategies to protect systems against quantum attacks, and approaches for combining pre-quantum cryptography with PQC to minimize transition risks. We suggest standards to start experimenting with now and provide a series of other recommendations to allow organizations to achieve a smooth and timely PQC transition.

Secure IoT in the Era of Quantum Computers-Where Are the Bottlenecks?

Recent progress in quantum computers severely endangers the security of widely used public-key cryptosystems and of all communication that relies on it. Thus, the US NIST is currently exploring new post-quantum cryptographic algorithms that are robust against quantum computers. Security is seen as one of the most critical issues of low-power IoT devices—even with pre-quantum public-key cryptography—since IoT devices have tight energy constraints, limited computational power and strict memory limitations. In this paper, we present, to the best of our knowledge, the first in-depth investigation of the application of potential post-quantum key encapsulation mechanisms (KEMs) and digital signature algorithms (DSAs) proposed in the related US NIST process to a state-of-the-art, TLS-based, low-power IoT infrastructure. We implemented these new KEMs and DSAs in such a representative infrastructure and measured their impact on energy consumption, latency and memory requirements during TLS handshakes on an IoT edge device. Based on our investigations, we gained the following new insights. First, we show that the main contributor to high TLS handshake latency is the higher bandwidth requirement of post-quantum primitives rather than the cryptographic computation itself. Second, we demonstrate that a smart combination of multiple DSAs yields the most energy-, latency- and memory-efficient public key infrastructures, in contrast to NIST’s goal to standardize only one algorithm. Third, we show that code-based, isogeny-based and lattice-based algorithms can be implemented on a low-power IoT edge device based on an off-the-shelf Cortex M4 microcontroller while maintaining viable battery runtimes. This is contrary to much research that claims dedicated hardware accelerators are mandatory.

Analysing the potential of transport triggered architecture for lattice-based cryptography algorithms

Lattice-based structures offer numerous possibilities for post-quantum cryptography. Recently, many post-quantum cryptography algorithms have been built on hard lattice problems. The three of the remaining four algorithms in the final round of the NIST Standardization Process rely on lattice-based methods. However, suitable processor architectures for these algorithms have not been sufficiently investigated. This study examines the potential advantages of transport triggered architecture for these algorithms. We compare popular 64-bit RISC-V processors with our conceptual transport triggered architecture processor over reference software implementations. Our processor provides better results than RISC-V competitors, regardless of the algorithm. It seems to be up to 3× faster, 1.6×-2× smaller, and consumes 1.3×-3.6× less energy than the compared RISC-V cores. Thus, an alternative base architecture is proposed for post-quantum cryptography processor development for embedded systems. The most critical shortcoming of the proposed architecture is the lack of compatible intellectual property core support for system-on-chip designs. We share comparative analyses with test results for different core configurations.

Accelerating Falcon on ARMv8

Falcon is one of the promising digital-signature algorithms in NIST’s ongoing Post-Quantum Cryptography (PQC) standardization finalist. Computational efficiency regarding software and hardware is also the main criteria for PQC standardization. In this paper, we present an efficient Falcon software implementation on ARMv8 environment. Until now, most of the software optimization on PQC algorithms have been conducted on 32-bit ARM (Cortex-M4) and typical CPUs (Intel and AMD CPUs). However, ARMv8 including Cortex-A30, 50, and 70 series have been widely used for various IoT (Internet of Things) applications, Edge computing devices, and OBUs (On Board Units) in autonomous driving cars. For optimizing the performance of Falcon, we take full advantage of NEON engine which is a kind of parallel processing unit in ARMv8 MCU. The main computation in Falcon belongs to polynomial multiplications in Complex number domain and Integer domain. Typically, FFT (Fast Fourier Transformation)-based multiplication method and NTT (Number Theoriteic Transform)-based multiplication method have been widely used for efficient polynomial multiplications in Complex number domain and Integer domain, respectively. Thus, in order to enhance the overall performance of Falcon, we improve the FFT-based multiplication method and NTT-based multiplication method by utilizing NEON engine in ARMv8. Specifically, we parallelize the overall process (FFT/NTT transformation, pointwise multiplication, and inverse FFT/NTT transformation) of FFT-based polynomial multiplication method and NTT-based polynomial multiplication method with strategically utilizing the NEON engine and vector instructions. Furthermore, we minimize the number of redundant memory accesses during FFT/NTT-based polynomial multiplication by making the most of available registers in NEON engine. Through the proposed parallel FFT/NTT-based polynomial multiplications, the proposed Falcon software provides 15.1% (resp. 18.1%), 16.5% (resp. 17.1%), and 65.4% (resp. 69.4%) of performance improvement in keypair generation, signing, and verification at security level 1 (resp. 5) compared with the reference Falcon implementation submitted to the final round of NIST PQC competition. Furthermore, as far as we know, this is the first optimized implementation of Falcon on ARMv8 environment.

FPGA Accelerated Post-Quantum Cryptography

Recent advancement in quantum information processing technology has led to the emergence of advanced cryptography in the post-quantum era. Next generation cryptographic techniques aim to be mathematically resistant against any known attacks related to quantum computing, and can be easily implemented on traditional hardware platforms. The National Institutes of Standards and Technology (NIST) has entered the fourth-round standardization process of post-quantum cryptography (PQC). Software implementations of PQC candidates have been widely investigated. Interests in domain-specific hardware acceleration of PQC algorithms have risen, in particular using field-programmable gate arrays (FPGAs). While conventional general-purpose hardware platforms have been used for PQC implementations, modern FPGAs promise software-hardware co-optimisation, deep pipeline parallelism and trivial support for custom-precision arithmetic. Therefore, the time is ripe for reviewing recent FPGA-based PQC implementations. This article first surveys state-of-the-art advances in PQC implementations on FPGAs, including fast arithmetic, algorithm-hardware codesign approaches and open-source PQC hardware projects, then gives a brief review of recent attacks on PQC algorithms and their hardware implementations. Finally, we summarise the challenges for hardware implementations along with potential research directions in this promising field.

Post-Quantum Blockchain-Based Secure Service Orchestration in Multi-Cloud Networks

Existing network service provisioning and lifecycle management (LCM) workflows rely on heterogeneous devices from multiple vendors and collaboration between multiple network actors, which can lead to numerous trust management and interoperability issues. Blockchain networks (BCNs) are a revolutionary way to establish trust in untrusted environments. In this complex environment, BCNs can help ensure transparency and security for network service LCM. However, BCNs are also vulnerable to quantum attacks. Advances in quantum computing will challenge the security of existing blockchain technology based on Public Key Infrastructure (PKI) technologies. In this paper, we explore how network services can be managed in a multiple administrative scenario. Our approach uses BCNs to track the operational steps of network service instantiation metrics while benefiting from the security features of post-quantum cryptography (PQC). Together with the use of N-th degree Truncated polynomial Ring Units (NTRU) as an example of a PQC algorithm that relies on the parallelization power of the Toom-Cook computation method with different security levels, we have shown that Quorum can provide a lower average time-to-write value compared to other BCNs considered (Ethereum and Hyperledger). At the end of the paper, we discuss the evaluation results and future directions regarding the coexistence of PQC algorithms and BCNs for network service orchestration and service federation between multiple administrative domains.

Analysis of the applicability of artificial neural networks for the post-quantum cryptography algorithms development

This article discusses the mathematical apparatus of artificial neural networks (ANNs) and analyzes the possibility of its application in the implementation of post-quantum asymmetric cryptosystems. The authors show that ANNs can be used for development such systems and analysis basic terms and processes in ANNs.

Development of a protocol for a closed mobile internet channel based on post-quantum algorithms

The development of computing technologies has made it possible not only to expand the range of mobile communication services, but also to significantly increase computing capabilities. The emergence of mobile Internet, 4G, 5G technologies makes it possible to talk about a fundamentally different approach to ensuring the quality of service to network customers, creating fundamentally new approaches to ensuring the efficiency and reliability of transmitted information flows. However, such a rapid growth of GSM technologies without the introduction of security services leads to active actions of attackers and cyber terrorists, the emergence of new and modification of known threats. Mobile communication channels are used by cybercriminals for selfish purposes of access to database resources not only of the mobile Internet, but also to the databases of information and communication systems and networks. The article proposes a fundamentally new approach to ensuring the closure of the voice channel of the mobile Internet based on post-quantum cryptography algorithms – McEliece and Niederreiter crypto-code constructions on elliptic codes. This approach provides not only the offline mode of closing the voice channel and creating a VPN channel in tunnel mode, but also the required level of cryptographic strength in the face of the emergence of full-scale quantum computers.

Development of a concept for building a critical infrastructure facilities security system

To effectively protect critical infrastructure facilities (CIF), it is important to understand the focus of cybersecurity efforts. The concept of building security systems based on a variety of models describing various CIF functioning aspects is presented. The development of the concept is presented as a sequence of solving the following tasks. The basic concepts related to cyberattacks on CIF were determined, which make it possible to outline the boundaries of the problem and determine the level of formalization of the modeling processes. The proposed threat model takes into account possible synergistic/emergent features of the integration of modern target threats and their hybridity. A unified threat base that does not depend on CIF was formed. The concept of modeling the CIF security system was developed based on models of various classes and levels. A method to determine attacker's capabilities was developed. A concept for assessing the CIF security was developed, which allows forming a unified threat base, assessing the signs of their synergy and hybridity, identifying critical CIF points, determining compliance with regulatory requirements and the state of the security system. The mathematical tool and a variety of basic models of the concept can be used for all CIFs, which makes it possible to unify preventive measures and increase the security level. It is proposed to use post-quantum cryptography algorithms on crypto-code structures to provide security services. The proposed mechanisms provide the required stability (230–235 group operations), the rate of cryptographic transformation is comparable to block-symmetric ciphers (BSC) and reliability (Perr 10–9–10–12)

Timing-Optimized Hardware Implementation to Accelerate Polynomial Multiplication in the NTRU Algorithm

Post-quantum cryptographic algorithms have emerged to secure communication channels between electronic devices faced with the advent of quantum computers. The performance of post-quantum cryptographic algorithms on embedded systems has to be evaluated to achieve a good trade-off between required resources (area) and timing. This work presents two optimized implementations to speed up the NTRUEncrypt algorithm on a system-on-chip. The strategy is based on accelerating the most time-consuming operation that is the truncated polynomial multiplication. Hardware dedicated modules for multiplication are designed by exploiting the presence of consecutive zeros in the coefficients of the blinding polynomial. The results are validated on a PYNQ-Z2 platform that includes a Zynq-7000 SoC from Xilinx and supports a Python-based programming environment. The optimized version that exploits the presence of double, triple, and quadruple consecutive zeros offers the best performance in timing, in addition to considerably reducing the possibility of an information leakage against an eventual attack on the device, making it practically negligible.

Research and analysis of implementations of the NIST PQC competition second round candidates focused on the Xilinx FPGA family

Today, the question of the stability of modern existing cryptographic mechanisms to quantum algorithms of cryptanalysis in particular and quantum computers in general is quite acute. This issue is actively discussed at the international level. Therefore, to solve it, NIST USA has decided to organize and is currently holding a competition for candidates for post-quantum cryptographic algorithms NIST PQC. The result of the competition should be the adoption of various types of cryptographic algorithms for standardization, namely, asymmetric encryption, key encapsulation and electronic signature (at least one algorithm of each type). 82 algorithms were submitted by the start of the competition for the standardization process. Based on the minimum eligibility criteria defined by NIST, 69 algorithms were considered for the 1st round. Given several parameters, namely, security, cost, performance, implementation characteristics, etc., 43 and 11 algorithms were excluded at the end of the 1st and 2nd rounds, respectively, and the other 15 algorithms were left for participation in the 3rd round. The algorithms left in the 2nd round can be divided into 5 different categories depending on their mathematical basis: those based on the isogeny of elliptic curves, those based on algebraic lattices, those based on mathematical code, those based on multivariate transformations and those based on hash functions. Security is the main evaluation criterion that determines competition in the NIST competition, and it is clear that candidates' software implementations are focused mainly on it. However, it is extremely important that the algorithm has an effective hardware implementation. Timely identification of hardware inefficiencies will help focus the cryptographic community efforts on more promising candidates, potentially saving a large amount of time that can be spent on cryptanalysis. This paper discusses and compares the FPGAs of Xilinx family. Data on the implementation of the candidates of the 2nd round in the process of standardization of post-quantum cryptography NIST, which are focused on the FPGA of the Xilinx family, are presented and compared.

Research on Post-Quantum Cryptosystem Based on IoT Devices

With the emergence of quantum computers, public-key cryptographic algorithms commonly used in classical computers are no longer secure. However, the current post-quantum cryptographic algorithms are mainly concentrated on the desktop CPU of Intel and AMD. For the Internet of Things, which is increasingly widely used, the research on post-quantum cryptographic algorithms is still scarce. Based on the research of post-quantum cryptosystem, this paper explores the post-quantum key algorithm based on Internet of Things devices.

Survey of Lattice to Design Post Quantum Cryptographic Algorithm Using Lattice

Objective: Quantum algorithm are stronger and more secure than the classical computers not because they run on faster harder computers but also, they require fewer steps. With Quantum computers the attackers have high computing power and with quantum algorithm can easily break the cryptographic system. Lattice is regularly spaced grid of points stretching to infinity. Quantum safe security algorithms are resistant to both attacks caused by classical computers and the attack caused by quantum computers. Lattice based cryptography are the post quantum cryptographic standards which are resistant to the attacks from quantum computers hence has advantage of strong security and high efficiency. The main objective of the paper is to study lattice, lattice properties, lattice – based cryptographic algorithm to design new lattice based cryptographic algorithm which are quantum resistant in future. Methods: In this paper the lattice-based cryptography is discussed right from its seminal work to its efficient cryptographic schemes. Paper discusses what is lattice, lattice properties, lattice problem and algorithmic solution to lattice problem and lattice-based cryptography. Findings: After studying post quantum cryptographic algorithms using lattice it was found that lattice-based post quantum cryptographic algorithms are resistant to quantum computer attacks. Novelty: Paper discusses lattice, properties of lattice in a simple way. Widely used cryptographic algorithms like RSA, Diffie-Hellman Key exchange, Elliptic Curve Cryptography are not resistant to quantum computers attacks. Paper discusses the importance of post quantum algorithm using lattice that are resistant to quantum computer attacks.

Energy Efficiency Analysis of Post-Quantum Cryptographic Algorithms

Classical cryptographic schemes in use today are based on the difficulty of certain number theoretic problems. Security is guaranteed by the fact that the computational work required to break the core mechanisms of these schemes on a conventional computer is infeasible; however, the difficulty of these problems would not withstand the computational power of a large-scale quantum computer. To this end, the post-quantum cryptography (PQC) standardization process initiated by the National Institute of Standards and Technology (NIST) is well underway. In addition to the evaluation criteria provided by NIST, the energy consumption of these candidate algorithms is also an important criterion to consider due to the use of battery-operated devices, high-performance computing environments where energy costs are critical, as well as in the interest of green computing. In this paper, the energy consumption of PQC candidates is evaluated on an Intel Core i7-6700 CPU using PAPI, the Performance API. The energy measurements are categorized based on their proposed security level and cryptographic functionality. The results are then further subdivided based on the underlying mechanism used in order to identify the most energy-efficient schemes. Lastly, IgProf is used to identify the most energy-consuming subroutines within a select number of submissions to highlight potential areas for optimization.

Comparative analysis of one-time hash-based signatures

Hash-based signatures are a wide class of post-quantum cryptographic algorithms, their security is based on the complexity of collision and preimage search problems for cryptographic hash functions. The main advantages of this class are post-quantization, easy modification and a well-researched mathematical base. The disadvantages are large sizes of signatures and limited number of uses of one key pair. The most promising algorithms of this class include algorithms of the SPHINCS type, which have a complex structure, including, among others, a one-time Winternitz signature. The paper analyzes the existing one-time signature algorithms, both well-known Lamport and Winternitz schemes, taking into account modifications of the latter one, and alternative methods. An analysis of the security of modified algorithms has been shown, which showed that their security is based on the same mathematical basis as the security of the original algorithms. The one-time use requirement remains critical to the safety of each of the algorithms studied. The sizes of keys and signatures and computational complexity of various algorithms are compared, in what their basic differences consist. The modified algorithms do not add fundamentally new components in cryptosystems but they make it possible to achieve a certain optimization, shifting the conditions of space-time compromise. The extended Lamport signature is of a particular interest, having the same computational complexity and key sizes as the original algorithm, and at the same time allowing one to halve the signature size. In the context of the SPHINCS cryptosystem, the Winternitz signature remains the best option, since it allows the complete computation of the public key directly from the signature.

Analysis and research of digital signature algorithm Picnic

An important feature of the post-quantum period in cryptography is the significant uncertainty regarding the source data for cryptanalysis and counteraction in terms of the capabilities of quantum computers, their mathematical and software, as well as the application of quantum cryptanalysis to existing cryptotransformations and cryptoprotocols. Mathematical methods of digital signature (DS) have been chosen as the main methods of NIST USA, which have undergone significant analysis and substantiation in the process of extensive research by cryptographers and mathematicians at the highest level. They are described in detail and studied at the first stage of the US NIST International Competition. In the second round, a number of decisions were made to merge some candidates for the post-quantum DS standard. 9 candidates were left for further research at the 2nd round: Crystals-Dilithium, Falcon, GeMSS, LUOV, MQDSS, Picnic, qTESLA, Rainbow and SPHINCS+. Three of them (Dilithium, Falcon, qTeSLA) are based on the stability of algebraic lattices (Lattice-based), four (GeMSS, LUOV, MQDSS, Rainbow) are based on multivariate transformations (MQ-transformations), one (SPHINCS+) is based on the stability of hash-function, one (Picnic) is based on the stability of the hash-function and block stream ciphers. During the 2nd round of the US NIST Competition the following finalist algorithms and alternative algorithms were selected as digital signatures according to the results of research on promising post-quantum cryptographic algorithms. As finalists algorithms such DS algorithms as Crystals-Dilithium, Falcon and Rainbow. Alternative algorithms are GeMSS, Picnic and SPHINCS+ were selected. This paper studies the peculiarities of construction of the digital signature algorithm considered as a candidate for the promising post-quantum standard of the NIST PQC competition – Picnic, also it analyzes the protection of the algorithm from known attacks. Data from the comparison of post-quantum algorithms such as digital signature are given. The description of the Picnic algorithm and its parameters are given.

An Experimental Study of Building Blocks of Lattice-Based NIST Post-Quantum Cryptographic Algorithms

Security of currently deployed public-key cryptography algorithms is foreseen to be vulnerable against quantum computer attacks. Hence, a community effort exists to develop post-quantum cryptography (PQC) algorithms, most notably the NIST PQC standardization competition. In this work, we have investigated how lattice-based candidate algorithms fare when implemented in hardware. To achieve this, we have assessed 12 lattice-based algorithms in order to identify their basic building blocks. We assume the algorithms will be implemented in an application-specific integrated circuit (ASIC) platform and the targeted technology is 65 nm. To estimate the characteristics of each algorithm, we have assessed the following characteristics: memory requirements, use of multipliers, and use of hashing functions. Furthermore, for these building blocks, we have collected area and power figures for all studied algorithms by making use of commercial memory compilers and standard cells. Our results reveal interesting insights about the relative importance of each building block for the overall cryptosystem, which can be used for guiding ASIC designers when selecting an algorithm or when deciding where to focus optimization efforts such that the final design respects requirements and design constraints.

Side-Channel Analysis and Countermeasure Design on ARM-Based Quantum-Resistant SIKE

The implementations of post-quantum cryptographic algorithms have been newly explored, whereas, the protection against side-channel attacks shall be considered upfront, since it can have a non-negligible impact on security and performance. In this article, the security of supersingular isogeny key encapsulation (SIKE), a second-round candidate of NIST's on-going post-quantum standardization process, is thoroughly evaluated under side-channel analysis. First, the vulnerabilities of reference and optimized implementations of SIKE are thoroughly analyzed in terms of both horizontal and vertical side-channel leakage. After the optimized SIKE, which is based on Three-point Montgomery Differential Ladder algorithm, is proved to be constant-time and there is no horizontal leakage, a vertical vulnerability is analyzed based on the source code at the algorithmic level, and a theoretical differential power analysis (DPA) attack is proposed. In order to exploit this vulnerability, the differential electromagnetic attack (DEMA) is put into practice to extract the private key of SIKE based on a 32-bit ARM platform. To the best of our knowledge, this is the first practical side-channel attack at SIKE implemented on real ARM-based devices. Our experiments show that the DEMA needs only hundreds of electromagnetic traces to carry out the attack. More importantly, an efficient window-based countermeasure is proposed to eliminate the vertical leakage and prevent side-channel attacks with only a little overhead. The security of our countermeasure is carefully evaluated against most of well-known power analysis attacks. Through careful evaluation and comparison with other countermeasures, this method can lead to higher security at a very small cost in terms of time and memory.