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.

The efficiency of polynomial multiplication execution majorly impacts the performance of lattice-based post-quantum cryptosystems. In this research, we propose a high-speed hardware architecture to accelerate polynomial multiplication based on the Number Theoretic Transform (NTT) in CRYSTAL-Kyber and CRYSTAL-Dilithium. We design a Digital Signal Processing (DSP) architecture for modular multiplication in butterfly and Point-Wise Multiplication (PWM) operations. Our method reduces the critical path delay of an n-bit multiplier to that of a (2n-2)-bit adder, optimizing both area and speed. These dedicated DSPs are employed in butterfly and PWM operations, completely eliminating the pre-process and post-process of NTT transforms. Furthermore, we introduce a novel unified pipelined architecture for the NTT and Inverse NTT (INTT) transformations of Kyber and Dilithium, with corresponding high-speed (Radix-2) and ultra high-speed (Radix-4) versions. Lastly, we construct a complete hardware accelerator for polynomial matrix-vector multiplication in Kyber. The Field-Programmable Gate Array (FPGA) implementation results have proven that our designs have significantly improved execution time by 3.4×–9.6× for the NTT transforms in Dilithium and 1.36×–34.16× for Kyber polynomial multiplication, compared to previous studies reported to date. Additionally, the hardware footprint results indicate that our proposed architectures exhibit superior hardware performance in Area-Time-Product (ATP), corresponding to a 44%–96% improvement. The proposed architectures are efficient and well-suited for high-performance lattice-based cryptography systems.

Transport Layer Security (TLS) provides a secure channel for end-to-end communications in computer networks. The ChaCha20–Poly1305 cipher suite is introduced in TLS 1.3, mitigating the sidechannel attacks in the cipher suites based on the Advanced Encryption Standard (AES). However, the few implementations cannot provide sufficient speed compared to other encryption standards with Authenticated Encryption with Associated Data (AEAD). This paper shows ChaCha20 and Poly1305 primitives. In addition, a compatible ChaCha20–Poly1305 AEAD with TLS 1.3 is implemented with a fault detector to reduce the problems in fragmented blocks. The AEAD implementation reaches 1.4-cycles-per-byte in a standalone core. Additionally, the system implementation presents 11.56-cycles-per-byte in an RISC-V environment using a TileLink bus. The implementation in Xilinx Virtex-7 XC7VX485T Field-Programmable Gate-Array (FPGA) denotes 10,808 Look-Up Tables (LUT) and 3731 Flip-Flops (FFs), represented in 23% and 48% of ChaCha20 and Poly1305, respectively. Finally, the hardware implementation of ChaCha20–Poly1305 AEAD demonstrates the viability of using a different option from the conventional cipher suite based on AES for TLS 1.3.

Quantum computing raises questions about the security of data encrypted using modern methods. Hence, the National Institute of Standards and Technology (NIST) has undertaken standardization of post-quantum cryptography (PQC) algorithms to defend against attacks from both classical and quantum computers. Following four rounds of evaluation, CRYSTALS-Kyber has been selected for standardization. In this paper, we present an efficient hardware architecture of CRYSTALS-Kyber for resource-constrained IoT devices. Firstly, we propose a compact hash module for CRYSTALS-Kyber. A single buffer is designed to perform padding, hashing, and holding data. Hence, using large FIFOs for data input/output is eliminated. Then, we propose a novel non-memory-based iterative number theoretic transform (NMI-NTT) architecture. Finally, the data flow between modules is optimized to improve parallelization and execution time. Implementation results on an Artix-7 FPGA show that our design consumes minimal hardware resources compared to the designs reported to date, corresponding to 5487 LUTs, 3426 FFs, 1548 SLICEs, 3.5 BRAMs, and 2 DSPs. Our design computes key generation, encapsulation, and decapsulation phases in 3.3/4.5/6.1 K-cycles for Kyber512, 5.6/7.1/9.2 K-cycles for Kyber768, and 8.5/10.1/12.9 K-cycles for Kyber1024, with 185MHz operating frequency. Our area-time-product (ATP) performance outperforms other designs.

The number of IoT devices has grown significantly in recent years, and edge computing in IoT is considered a new and growing trend in the technology industry. While cryptography is widely used to enhance the security of IoT devices, it also carries limitations such as resource constraints or latency. Therefore, lightweight cryptography (LWC) balances commensurate resource usage and maintaining security while minimizing system costs. The ASCON stands out among the LWC algorithms as a potential target for implementation and cryptoanalysis. It provides authenticated encryption with associated data (AEAD) and hashing functionalities in many variants, aiming for various applications. In this brief, we present an implementation of Ascon cryptography as a peripheral of a RISC-V System-on-a-Chip (SoC). The ASCON crypto core occupies 1,424 LUTs in FPGA and 17.4 kGE in 180nm CMOS technology while achieving 417 Gbits/J energy efficiency at a supply voltage of 1.0V and frequency of 2 MHz.

The Number Theoretic Transform (NTT) has been widely used to speed up polynomial multiplication in lattice-based post-quantum algorithms. All NTT operands use modular arithmetic, especially modular multiplication, which significantly influences NTT hardware implementation efficiency. Until now, most hardware implementations used Digital Signal Processing (DSP) to multiply two integers and optimally perform modulo computations from the multiplication product. This paper presents a customized Lattice-DSP (L-DSP) for modular multiplication based on the Karatsuba algorithm, Vedic multiplier, and modular reduction methods. The proposed L-DSP performs both integer multiplication and modular reduction simultaneously for lattice-based cryptography. As a result, the speed and area efficiency of the L-DSPs are 283 MHz for 77 SLICEs, 272 MHz for 87 SLICEs, and 256 MHz for 101 SLICEs with the parameters q of 3329, 7681, and 12,289, respectively. In addition, the $N^{-1}$ multiplier in the Inverse-NTT (INTT) calculation is also eliminated, reducing the size of the Butterfly Unit (BU) in CRYSTAL-Kyber to about 104 SLICEs, equivalent to a conventional multiplication in the other studies. Based on the proposed DSP, a Point-Wise Matrix Multiplication (PWMM) architecture for CRYSTAL-Kyber is designed on a hardware footprint equivalent to 386 SLICEs. Furthermore, this research is the first DSP designed for lattice-based Post-quantum Cryptography (PQC) modular multiplication.