Evaluation and Comparison of Lattice-Based Cryptosystems for a Secure Quantum Computing Era

Sabani, Maria; Savvas, Ilias Κ.; Poulakis, Dimitrios; Garani, Georgia; Makris, Georgios C.

doi:10.3390/electronics12122643

Cited by 5 publications

(12 citation statements)

References 62 publications

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“…Lattice algorithms have an advantage over code-based algorithms due to their shorter key size, making them more appropriate for low-constrained devices. Furthermore, the algorithms employed in lattice-based cryptosystems are distinguished by their simplicity, efficiency, and high parallelizability [42]. The cryptographic protocols grounded in lattice structures have demonstrated robust security, relying on established lattice problems such as the shortest vector problem (SVP) and the learning with errors problem (LWE) [42].…”

Section: Isogeny-based Cryptographymentioning

confidence: 99%

“…Furthermore, the algorithms employed in lattice-based cryptosystems are distinguished by their simplicity, efficiency, and high parallelizability [42]. The cryptographic protocols grounded in lattice structures have demonstrated robust security, relying on established lattice problems such as the shortest vector problem (SVP) and the learning with errors problem (LWE) [42]. These factors collectively position lattice-based cryptographic schemes as a dynamic and leading area of exploration in post-quantum cryptography considered the most prominent and promising.…”

Section: Isogeny-based Cryptographymentioning

confidence: 99%

“…In the literature, numerous papers have conducted comparisons among lattice-based post-quantum cryptographic algorithms [42][43][44]. From these papers, we extract information for Table 3, which presents a comparative analysis of SABER, CRYSTALS-Kyber, NTRU, and FrodoKEM post-quantum algorithms.…”

Section: Isogeny-based Cryptographymentioning

confidence: 99%

“…However, CRYSTALS-KYBER outperforms NTRU in terms of CPU usage, while NRTU excels in small key sizes compared to CRYSTAL-KYBER. Notably, a key advantage of NTRU is its commercial implementation [42], indicating a well-established understanding of its security since its initial publication in 1996. In the next subsection, a description of the NTRU public encryption algorithm is detailed.…”

Section: Isogeny-based Cryptographymentioning

confidence: 99%

“…Considered resilient to quantum computer attacks, particularly Shor's attack [43], NTRU stands out as a prominent post-quantum cryptosystem. It is designed to resist various types of attacks, including lattice basis reduction, meet-in-the-middle attacks, and chosen ciphertext attacks [42]. Ongoing cryptanalysis efforts continually examine NTRU, leading to the development of various attack strategies [42].…”

Section: Ntru Security Analysismentioning

confidence: 99%

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Lightweight Computational Complexity Stepping Up the NTRU Post-Quantum Algorithm Using Parallel Computing

Elkabbany,

Ahmed,

Aslan

et al. 2023

Symmetry

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The Nth-degree Truncated polynomial Ring Unit (NTRU) is one of the famous post-quantum cryptographic algorithms. Researchers consider NTRU to be the most important parameterized family of lattice-based public key cryptosystems that has been established to the IEEE P1363 standards. Lattice-based protocols necessitate operations on large vectors, which makes parallel computing one of the appropriate solutions to speed it up. NTRUEncrypt operations contain a large amount of data that requires many repetitive arithmetic operations. These operations make it a strong candidate to take advantage of the high degree of parallelism. The main costly operation that is repeated in all NTRU algorithm steps is polynomial multiplication. In this work, a Parallel Post-Quantum NTRUEncrypt algorithm called PPQNTRUEncrypt is proposed. This algorithm exploits the capabilities of parallel computing to accelerate the NTRUEncrypt algorithm. Both analytical and Apache Spark simulation models are used. The proposed algorithm enhanced the NTRUEncrypt algorithm by approximately 49.5%, 74.5%, 87.6%, 92.5%, 93.4%, and 94.5%, assuming that the number of processing elements is 2, 4, 8, 12, 16, and 20 respectively.

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Section: Isogeny-based Cryptographymentioning

confidence: 99%

Section: Isogeny-based Cryptographymentioning

confidence: 99%

Section: Isogeny-based Cryptographymentioning

confidence: 99%

Section: Isogeny-based Cryptographymentioning

confidence: 99%

Section: Ntru Security Analysismentioning

confidence: 99%

See 3 more Smart Citations

Lightweight Computational Complexity Stepping Up the NTRU Post-Quantum Algorithm Using Parallel Computing

Elkabbany,

Ahmed,

Aslan

et al. 2023

Symmetry

View full text Add to dashboard Cite

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Near Threshold Computation of Partitioned Ring Learning With Error (RLWE) Hardware Accelerator on Reconfigurable Architecture

Baidya,

Mandal,

Paul

2024

IEEE Access

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The Ring Learning With Error (RLWE) algorithm plays a crucial role in Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE). The security of existing classical crypto algorithms is reduced in quantum computers. The adversaries can store all encrypted data and once quantum computers become available, they can potentially expose this encrypted data. Researchers and cryptographers are actively developing and exploring quantum-resistant cryptographic algorithms like RLWE to address this emerging threat. On the other hand, the HE allows operations on encrypted data, which is appropriate for getting services from third parties without revealing confidential plain-texts. Field Programmable Gate Array (FPGA) based Post-Quantum Cryptography (PQC) and Homomorphic Encryption (HE) hardware accelerators, such as Ring Learning With Error (RLWE), offer a much cost-effective alternative to processorbased platforms and Application-Specific Integrated Circuits (ASIC). However, FPGA based hardware accelerators still consume more power compared to ASIC based design. Near Threshold Computation (NTC) may be a convenient solution for FPGA based RLWE implementation. This paper implements a low-power RLWE hardware accelerator in an FPGA, operating at near-threshold biasing voltage. Instead of applying uniform biasing voltage to all 14 subcomponents of RLWE, this paper applies different near-threshold biasing voltages to the different subcomponents of proposed RLWE. Based on the longest design path or critical path of the 14 subcomponents of the proposed RLWE, the entire RLWE is partitioned into different clusters where each cluster is implemented in an FPGA partition. All the subcomponents placed in the same FPGA partition use the same biasing voltage V ccint . The clusters that have higher critical paths use higher V ccint to avoid timing failure. The clusters that have lower critical paths use lower biasing voltage V ccint . The proposed RLWE uses a voltage calibration algorithm to calculate the biasing voltage V ccint required for a certain amount of average critical path of a FPGA partition. Any timing error caused by NTC can be detected by the Razor flip-flop used in each subcomponent of RLWE. This voltage scaled, partitioned RLWE can save ∼6% and ∼11% power in Vivado and VTR platforms, respectively. Although low-power RLWE is the primary focus, the resource usage and throughput of the implemented RLWE hardware accelerator are competitive with existing literature. INDEX TERMSFPGA, Low Power, Post Quantum Cryptography, Ring Learning With Error I. INTRODUCTION Lattice-based cryptography is currently considered one of the most secure solutions compared to classical cryptography schemes. Classical schemes such as the discrete logarithm (used in Elliptic Curve Cryptography), RSA and ECDSA are employed to secure modern Internet communications. These asymmetric key crypto-systems are based on the hardness of the prime factor and discrete logarithm. However, asymmet-ric key crypto-systems are no longer secure under quantum attacks...

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Illuminating the Path of Post-Quantum Cryptographic Protocols: A Survey of some Recent Literatures

Kefas,

Mishra,

Kant

2023

Preprint

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The imminent threat posed by quantum computers to modern public key cryptography has spurred the development of post-quantum cryptography (PQC) algorithms. Over the last two decades, the field of PQC research has thrived, yielding a diverse range of algorithms resilient against quantum attacks. These PQC algorithms are undergoing selection and standardization by prominent bodies ; such as National Institute of Standards and Technology (NIST). However, the challenge remains substantial, given the monumental task of migrating numerous new devices to PQC algorithms. This complex, multi-decade transition from classical cryptography to PQC, necessitates careful survey of research articles to consider the current post quantum cryptographic schemes, and key protective strategies against quantum threats, implementation feasibility, compliance and challenges of implementations. This will provide insight and future directions for new researchers and organizations. .

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Evaluation and Comparison of Lattice-Based Cryptosystems for a Secure Quantum Computing Era

Cited by 5 publications

References 62 publications

Lightweight Computational Complexity Stepping Up the NTRU Post-Quantum Algorithm Using Parallel Computing

Lightweight Computational Complexity Stepping Up the NTRU Post-Quantum Algorithm Using Parallel Computing

Near Threshold Computation of Partitioned Ring Learning With Error (RLWE) Hardware Accelerator on Reconfigurable Architecture

Illuminating the Path of Post-Quantum Cryptographic Protocols: A Survey of some Recent Literatures

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