Lattice-based cryptography (LBC) is one of the most promising classes of post-quantum cryptography (PQC) that is being considered for standardization. This brief proposes an optimized schoolbook polynomial multiplication (SPM) for compact LBC. We exploit the symmetric nature of Gaussian noise for bit reduction. Additionally, a single field-programmable gate array (FPGA) DSP block is used for two parallel multiplication operations per clock cycle. These optimizations enable a significant 2.2× speedup along with reduced resources for dimension n = 256. The overall efficiency (throughput per slice) is 1.28× higher than the conventional SPM, as well as contributing to a more compact LBC system compared to previously reported designs. The results targeting the FPGA platform show that the proposed design can achieve high hardware efficiency with reduced hardware area costs.

Lattice-based cryptography (LBC) has emerged as the most viable substitutes to the classical cryptographic schemes as 5 out of 7 finalist schemes in the 3rd round of the NIST post-quantum cryptography (PQC) standardization process are lattice based in construction. This work explores novel architectural optimizations in the FPGA-based hardware implementation of polynomial multiplication, which is a bottleneck in every LBC construction. To target ultra-high throughput, both schoolbook polynomial multiplication (SPM) and number theoretic transform (NTT) are explored: a completely parallel architecture of an SPM is undertaken while for NTT, radix-2 and radix-22 multi-path delay commutator (MDC) based pipelined architectures are adopted. Our proposed high-speed SPM (HSPM) structure on latest Xilinx UltraScale+ FPGA is 5 faster than the state-of-the-art LBC designs. Whereas, the proposed high-speed NTT (HNTT) structure (i.e., R22MDC) takes only 0.63s for the encryption, hence achieving the highest throughput of 408 Mbps. Moreover, all of the proposed designs achieve highest design efficiencies (i.e., throughput per slice (TPS)) in comparison to available LBC designs.

CRYSTALS-Kyber (Kyber) was recently chosen as the first quantum resistant Key Encapsulation Mechanism (KEM) scheme for standardisation, after three rounds of the National Institute of Standards and Technology (NIST) initiated PQC competition which begin in 2016 and search of the best quantum resistant KEMs and digital signatures. Kyber is based on the Module-Learning with Errors (M-LWE) class of Lattice-based Cryptography, that is known to manifest efficiently on FPGAs. This work explores several architectural optimizations and proposes a high-performance and area-time (AT) product efficient hardware accelerator for Kyber. The proposed architectural optimizations include inter-module and intra-module pipelining, that are designed and balanced via FIFO based buffering to ensure maximum parallelisation. The implementation results show that compared to state-of-the-art designs, the proposed architecture delivers 25-51% speedups for Kyber’s three different security levels on Artix-7 and Zynq UltraScale+ devices, and a 50-75% reduction in DSPs at comparable security level. Consequently, the proposed design achieve higher AT product efficiencies of 19-33%.

Lattice-based cryptography (LBC) is a promising and efficient public key cryptography scheme whose theoretical foundation usually lies in Learning with Error (LWE) problem and its variant such as Ring-LWE (R-LWE) is the most studied cryptosystem which allows for more efficient implementation while maintaining the hardness of an original problem. Polynomial multiplication is the bottleneck of R-LWE, that can either be done using Number Theoretic Transform (NTT) or schoolbook polynomial multiplication (SPM) algorithm. The use of SPM is wider and possible for all parameters of R-LWE schemes. This work proposes an efficient and parallel strategy for SPM in R-LWE; by successfully reducing its time complexity from n2 to n2/4 (making it 1.8× faster and 1.4× hardware efficient). Furthermore, by adjusting the bit width for the error terms, the polynomial multiplication and addition blocks are reused for both encryption and decryption modules resulting in 14% reduced area and 1.7× better throughput in comparison to state-of-art SPM based R-LWE designs.

Cryptographic co-processors are integral to the modern System-on-Chips. Flexibility in such designs serves dual purpose, i.e., it enables acceleration of different essential cryptographic primitives (Encryption/Authentication/Pseudo Random Number Generation (PRNG)) and also results in design compaction via resource sharing. In this context, a novel resource-shared crypto-coprocessor, named AE$HA-3 is presented, which combines two National Institute of Standards and Technology (NIST) standardized algorithms, i.e., Advance Encryption Standard (AES) and Secure Hash Algorithm-3 (SHA-3). Due to algorithmic dissimilarities, so far no resource-shared implementation enabling AES key scheduling/ enc/dec and SHA-3 has been presented. AE$HA-3 exploits resource-sharing for area reduction, i.e., integration of Look-Up-Tables (I-Tables) for AES enc/dec; logical optimization of Six Input Equation (SixIE) for SHA-3; a Unified XOR Section to carry out both key whitening in AES and SHA-3 transformations. Furthermore, the AES key scheduling was performed using the same resource-shared hardware. The proposed AE$HA-3 on Xilinx Virtex FPGA family results in highest hardware efficiency in terms of Throughput per Slice (TPS), along with a 49.37% area consumption reduction, when compared against the smallest stand-alone implementations presented to date.

The Internet of Things (IoT) nodes consist of sensors that collect environmental data and then perform data exchange with surrounding nodes and gateways. Cybersecurity attacks pose a threat to the data security that is being transmitted in any IoT network. Cryptographic primitives are widely adopted to address these threats; however, the substantial computation demands limit their applicability in the IoT ecosystem. In addition, each IoT node varies with respect to the area and throughput (TP) requirements, thus demanding flexible implementation for encryption/decryption processes. To solve these issues, this work implements the NIST lightweight cryptography standard, Ascon, on a SAED 32 nm process design kit (PDK) library by employing loop folded, loop unrolled and fully unrolled architectures. The fully unrolled architecture can achieve the highest TP but at the cost of higher area utilisation. Unrolling by a lower factor results in lower area implementations, enabling the exploration of design space to tackle the trade-off between area and TP performance of the design. The implementation results show that, for loop folded architecture, Ascon-128 and Ascon-128a require 36.7k $$\upmu \textrm{m}^{2}$$μ m 2 and 38.5k $$\upmu \textrm{m}^{2}$$μ m 2 chip area, respectively compared to 277.1k $$\upmu \textrm{m}^{2}$$μ m 2 and 306.6k $$\upmu \textrm{m}^{2}$$μ m 2 required by their fully unrolled implementations. The proposed implementation strategies can adjust the number of rounds to accommodate the varied requirements of IoT ecosystems. An implementation with an open-source 45 nm PDK library is also undertaken for enhanced generalization and reproducibility of the results.