BUFF Transform for Isogeny-Based Sqisign Digital Signature

In the post-quantum era, post-quantum cryptography (PQC) processors are required to ensure quantum-secure communication and e-commerce with high throughput, while maintaining adequate flexibility to execute different crypto-primitives, such as key encapsulation mechanism (KEM) and digital signature (DS) at multiple security levels with evolving modifications. The PQC standards, which are based on multiple mathematical problems, will be available around the end of 2021 in NIST's PQC standardization (Fig. 34.1.1). Crypto-agility, coupled with new mathematical calculations, high computing complexity, and large memory consumption brings challenges to the design of PQC processors considering flexibility, throughput, and energy efficiency.

NIST is in the process of evaluating public-key digital signature algorithms for potential standardization to protect sensitive information into the foreseeable future, including after the advent of quantum computers. Any signature scheme that is eventually selected would augment FIPS 204, Module-Lattice-Based Digital Signature Standard; FIPS 205, Stateless Hash-Based Digital Signature Standard; FIPS 186-5, Digital Signature Standard (DSS); and SP 800-208, Recommendation for Stateful Hash-Based Signature Schemes. This report describes the evaluation criteria and selection process of the First Round of the Additional Digital Signatures for the NIST Post-Quantum Cryptography (PQC) Standardization Process. Based on public feedback and internal reviews of the first-round candidates, NIST selected14 candidate algorithms to move forward to the second round of evaluation: CROSS, FAEST, HAWK, LESS, MAYO, Mirath (merger of MIRA/MiRitH), MQOM, PERK, QR-UOV, RYDE, SDitH, SNOVA, SQIsign, and UOV.

The advancements in quantum computing and the potential for polynomial-time solutions to traditional public key cryptography (i.e., Rivest–Shamir–Adleman (RSA) and elliptic-curve cryptography (ECC)) using Shor’s algorithm pose a serious threat to the security of pre-quantum blockchain technologies. This paper proposes an efficient quantum-safe blockchain that incorporates new quantum-safe consensus algorithms. We integrate post-quantum signature schemes into the blockchain’s transaction signing and verification processes to enhance resistance against quantum attacks. Specifically, we employ the Falcon signature scheme, which was selected during the NIST post-quantum cryptography (PQC) standardization process. Although the integration of the post-quantum signature scheme results in a reduction in the blockchain’s transactions per second (TPSs), we introduce efficient approaches to mitigate this performance degradation. Our proposed post-quantum delegated proof of luck (PQ-DPoL) combines a proof of luck (PoL) mechanism with a delegated approach, ensuring quantum resistance, energy efficiency, and fairness in block generation. Experimental results demonstrate that while post-quantum cryptographic algorithms like Falcon introduce larger signature sizes and slower processing times, the PQ-DPoL algorithm effectively balances security and performance, providing a viable solution for secure blockchain operations in a post-quantum era.

Classic McEliece has gathered attention as a candidate in NIST post-quantum cryptography standardization. However, it suffers from high demands on the decryption algorithm, making it unsuitable for resource-constrained devices. In this paper, we propose a novel implementation method, named giant footprint sharing, that reduces memory size during decryption in Classic McEliece. The decryption algorithm processes a large number of intermediate variables computed from a secret key in memory. The giant footprint sharing identifies the largest variable among them and allocates a memory-sharing structure to store it, thereby reducing the overall memory size regardless of the implementation platform. The giant footprint sharing can also be combined with existing acceleration techniques, such as fast Fourier transformation. We evaluate Classic McEliece with the giant footprint sharing on the Arm Cortex-M33 CPU and show that it reduces memory size by up to 46% without significant degradation in computation time compared with the existing fast-implementation by Chen et al. (at TCHES 2021). Extensive experiments with the giant footprint sharing further reveal that it maintains a constant memory size regardless of the compiler optimization, and it also achieves an optimal balance in the trade-off between memory size and computation time. The giant footprint sharing is remarkable for any scheme, that contains a large-scale matrix computation and the life cycle for each variable is limited.

Post-Quantum Cryptography (PQC) has emerged as a response of the cryptographic community to the danger of attacks performed using quantum computers. All PQC schemes can be implemented in software and hardware using conventional (non-quantum) computing systems. PQC is the biggest revolution in cryptography since the invention of public-key schemes in the mid-1970 s. Lattice-based key exchange schemes have emerged as leading candidates in the NIST PQC standardization process due to their relatively short public keys and ciphertexts. This paper presents novel high-speed hardware architectures for four lattice-based Key Encapsulation Mechanisms (KEMs) representing three NIST PQC finalists: NTRU (with two distinct variants, NTRU-HPS and NTRU-HRSS), CRYSTALS-Kyber, and Saber. We benchmark these candidates in terms of their performance and resource utilization in today's FPGAs. Our best architectures outperform the best designs from other groups reported to date in terms of the area-time product by factors ranging from 1.01 to 2.88, depending on the algorithm and security level. Additionally, our study demonstrates that CRYSTALS-Kyber and Saber have very similar hardware performance. Both outperform NTRU in terms of execution time by a factor 36-62 for key generation and 3-7 for decapsulation, assuming the same security level.

The National Institute of Standards and Technology is in the process of selecting public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify additional digital signature, public-key encryption, and key-establishment algorithms to augment Federal Information Processing Standard (FIPS) 186-4, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers. The first round of the NIST Post-Quantum Cryptography Standardization Process began in December 2017 with 69 candidate algorithms that met both the minimum acceptance criteria and submission requirements. The first round lasted until January 2019, during which candidate algorithms were evaluated based on their security, performance, and other characteristics. NIST selected 26 algorithms to advance to the second round for more analysis. The second round continued until July 2020, after which seven 'finalist' and eight 'alternate' candidate algorithms were selected to move into the third round. This report describes the evaluation and selection process, based on public feedback and internal review, of the third-round candidates. The report summarizes each of the 15 third-round candidate algorithms and identifies those selected for standardization, as well as those that will continue to be evaluated in a fourth round of analysis. The public-key encryption and key-establishment algorithm that will be standardized is CRYSTALS-Kyber. The digital signatures that will be standardized are CRYSTALS-Dilithium, Falcon, and SPHINCS+. While there are multiple signature algorithms selected, NIST recommends CRYSTALS-Dilithium as the primary algorithm to be implemented. In addition, four of the alternate key-establishment candidate algorithms will advance to a fourth round of evaluation: BIKE, Classic McEliece, HQC, and SIKE. These candidates are still being considered for future standardization. NIST will also issue a new Call for Proposals for public-key digital signature algorithms to augment and diversify its signature portfolio.

Blockchain technology ensures accountability, transparency, and redundancy, but its reliance on public‐key cryptography makes it vulnerable to quantum computing threats. This article addresses the urgent need for quantum‐safe blockchain solutions by integrating post‐quantum cryptography (PQC) into blockchain frameworks. Utilizing algorithms from the NIST PQC standardization process, it is aimed to fortify blockchain security and resilience, particularly for IoT and embedded systems. Despite the importance of PQC, its implementation in blockchain systems tailored for embedded environments remains underexplored. A quantum‐secure blockchain architecture is proposed, evaluating various PQC primitives and optimizing transaction sizes through techniques such as public‐key recovery for Falcon, achieving up to 17% reduction in transaction size. The analysis identifies Falcon‐512 as the most suitable algorithm for quantum‐secure blockchains in computer‐based environments and XMSS as a viable but unsatisfactory stateful alternative. However, for embedded‐based blockchains, Dilithium demonstrates a higher transactions‐per‐second (TPS) rate compared to Falcon, primarily due to Falcon's slower signing performance on ARM CPUs. This highlights the signing time as a critical limiting factor within embedded blockchains. Additionally, smart contract functionality is integrated, assessing the impact of PQC on smart contract authentication. The findings demonstrate the feasibility and practicality, paving the way for robust and future‐proof IoT applications.

Homomorphic authenticated encryption allows implicit computation on plaintexts using corresponding ciphertexts without losing privacy, and provides authenticity of the computation and the resultant plaintext of the computation when performing a decryption. However, due to its special functionality, the security notions of the homomorphic authenticated encryption is somewhat complicated and the construction of fully homomorphic authenticated encryption has never been given. In this work, we propose a new security notion and the first construction of fully homomorphic authenticated encryption. Our new security notion is a unified definition for data privacy and authenticity of homomorphic authenticated encryption. Moreover, our security notion is simpler and stronger than the previous ones. To realize our new security notion, we also suggest a construction of fully homomorphic authenticated encryption via generic construction. We combine a fully homomorphic encryption and two homomorphic authenticators, one fully homomorphic and one OR-homomorphic, to construct a fully homomorphic authenticated encryption that satisfies our security notion. Our construction requires its fully homomorphic encryption to be indistinguishable under chosen plaintext attacks and its homomorphic authenticators to be unforgeable under selectively chosen plaintext queries. Our construction also supports multiple datasets and amortized efficiency. For efficiency, we also construct a multi-dataset fully homomorphic authenticator scheme, which is a variant of the first fully homomorphic signature scheme. Our multi-dataset fully homomorphic authenticator scheme satisfies the security requirement of our generic construction above and supports amortized efficiency.

A novel ID-based proxy-protected signature scheme based on identity information is presented in this paper. We review the concept ID-Based signature introduced by Shamir, define the security notion of an ID-Based signature. We also improve the Shamir’s ID-Based signature and prove its security under the proposed security notion. From the improved Shamir’s ID-Based signature scheme we construct an ID-Based proxy signature scheme, the security is based on the underlying ID-based signature scheme. Our scheme is efficient and easy to implement. The scheme simplifies the public key as the user’s id and can be easily applied to all the RSA-type cryptosystems.

With the gradual progress of NIST’s post-quantum cryptography standardization, the Round-1 KEM proposals have been posted for public to discuss and evaluate. Among the IND-CCA-secure KEM constructions, mostly, an IND-CPA-secure (or OW-CPA-secure) public-key encryption (PKE) scheme is first introduced, then some generic transformations are applied to it. All these generic transformations are constructed in the random oracle model (ROM). To fully assess the post-quantum security, security analysis in the quantum random oracle model (QROM) is preferred. However, current works either lacked a QROM security proof or just followed Targhi and Unruh’s proof technique (TCC-B 2016) and modified the original transformations by adding an additional hash to the ciphertext to achieve the QROM security.

With the development of the Internet of Things (IoT) and cloud computing technology, various cryptographic systems have been proposed to protect increasing personal information. Recently, Post-Quantum Cryptography (PQC) algorithms have been proposed to counter quantum algorithms that threaten public key cryptography. To efficiently use PQC in a server environment dealing with large amounts of data, optimization studies are required. In this paper, we present optimization methods for FrodoKEM and NewHope, which are the NIST PQC standardization round 2 competition algorithms in the Graphics Processing Unit (GPU) platform. For each algorithm, we present a part that can perform parallel processing of major operations with a large computational load using the characteristics of the GPU. In the case of FrodoKEM, we introduce parallel optimization techniques for matrix generation operations and matrix arithmetic operations such as addition and multiplication. In the case of NewHope, we present a parallel processing technique for polynomial-based operations. In the encryption process of FrodoKEM, the performance improvements have been confirmed up to 5.2, 5.75, and 6.47 times faster than the CPU implementation in FrodoKEM-640, FrodoKEM-976, and FrodoKEM-1344, respectively. In the encryption process of NewHope, the performance improvements have been shown up to 3.33 and 4.04 times faster than the CPU implementation in NewHope-512 and NewHope-1024, respectively. The results of this study can be used in the IoT devices server or cloud computing service server. In addition, the results of this study can be utilized in image processing technologies such as facial recognition technology.

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.

Over the years, important breakthroughs have been made in protecting data at rest or in-transit. The emergence of the Internet of Things (IoT) and Cyber Physical Systems (CPS) has pose new challenges for protecting data in systems and devices tightly close to humans. Embedded systems with constrained computing capabilities are a central part in IoT and CPS, susceptible to different security attacks and vulnerabilities. Lightweight cryptography is the term used for grouping the different cryptographic algorithms and techniques tailored to observe the requirements for data security in such constrained applications. Nowadays, the potential emergence of quantum computing threatens these security solutions widely in use. Thus, novel cryptographic algorithms deemed to resist quantum attack models are being standardized by the National Institute of Standards and Technology (NIST) in the Post-Quantum Cryptography (PQC) Standardization process. In this paper, we present a study on how the advent of quantum computing might have a deep impact on the security of constrained applications in the IoT and CPS domains. We focused on the NIST PQC finalists, from the perspective of their use for securing embedded systems.

CRYSTALS-Kyber is a quantum-resistant and promising lattice-based cryptography (LBC) in the finalists of the third round post-quantum cryptography (PQC) standardization, which is based on the hardness of Module-Learning with Errors (M-LWE). The variadic parameters make M-LWE obtain a more flexible security-performance trade-off than Ring-LWE. In this paper, we propose a M-LWE cryptoprocessor targeting CRYSTALS-Kyber with area-time trade-off for the first time. This balanced design includes a fast and low-cost Binomial Sampler and vector-polynomials multiplication structure based on pipelined decimation-in-frequency (DIF) based Number Theoretic Transform (NTT) technique. The M-LWE cryptoprocessor achieve 27,708 encryption operations per second using only 690 slices and 106,716 decryption operations per second using only 571 slices. Our proposed design achieved the lowest area-time product (ATP) with at least 2 χ performance improvement than the state-of-the-art LBC designs with a similar security level and complexity of polynomials.

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.