This work presents an enhanced two-step Correlation Power Analysis (CPA) attack targeting the recently standardised ML-KEM on an ARM Cortex M4. Our enhancement exploits the knowledge of intermittent variables to identify sample points of interest and develop bespoke attack functions. Step one targets the odd coefficients of each Secret Key Polynomial Vector ( ˆ s), before step two targets the remaining even coefficients using more elaborate attack functions. After successfully demonstrating key recovery for the first set of ˆ s, we then characterise leakage behaviour, revealing a trend indicating recovery of each coefficient becomes more efficient with subsequent iterations of the internal doublebasemul operation. By applying our enhanced two step attack methodology, we successfully recovered the entire key using only 179 traces, without the need for elaborate preconditions or ciphertext manipulations. We obtain remarkable results in the initial stage of our attack, while the second phase achieves performance comparable to other recent studies.

Multiplication is a core operation in various applications such as cryptography and machine learning. Dedicated DSP blocks are provided by FPGA vendors for multiplication. However, these DSP blocks are limited in number and their location on FPGA is fixed, resulting in routing delays that affects the performance for small size multipliers. In this paper, a high performance and resource efficient 5 × 5 multiplier is presented that utilizes lookup tables (LUTs) and fast carry chain of the FPGA. The proposed multiplier offers 30% reduction in LUTs compared to Vivado DSP-less inferred multiplier at the cost of a slight increase in critical path delay (CPD). The proposed multiplier requires lesser power consumption and has better area- delay product (ADP) and power-delay product (PDP) metrics. Based on the proposed multiplier, a finite field multiplier is developed for post quantum digital signatures such as QR-UOV, MAYO and MQOM. The matrix-vector architecture is the core operation in multivariate digital signatures and integration of our finite field multiplier in a matrix-vector architecture shows that area is almost halved compared to state-of-the-art.

Homomorphic encryption (HE) allows computations on encrypted data, making it desirable for use in privacy preserving data analytics. However, HE function evaluation is computationally intensive. Approximate computing (AC) allows a trade-off between accuracy, memory/energy usage and running time. Polynomial approximation of the Rectified Linear Unit (ReLU) function, a key CNN activation function, is explored andAC techniques of task-skipping and depth reduction are applied. The most accurate ReLU approximations are implemented in nGraph-HE’s Cryptonets CNN using a SEAL backend, resulting in a minimal decrease intraining accuracy of 0.0011, no change in plaintext classification accuracy, and a speed-up of 47%.

The dawn of cost-effective miniaturised satellites is currently attracting venture capital in a never seen before ratio to launch mega-constellations of satellites for a diverse range of applications. These satellites are vulnerable to attacks by high-capability cyber-criminals (including quantum enabled adversaries), due to the critical data they transmit. Additionally, space missions have long lifespan and a long lead time in terms of development process, requiring a pre-emptive outlook to ensuring their safety. In 2016, National Institute of Standards and Technology (NIST) initiated the competition to standardise the post-quantum cryptography (PQC) schemes, announcing the first portfolio of chosen schemes in 2022. This work targets the only public key exchange (PKE) scheme among the winners of the NIST-PQC standardisation process, CRYSTALS-Kyber, and implements its core bottleneck operation, i.e., number theoretic transform (NTT) extensively used for the polynomial multiplication. To avoid data corruption due to space based radiations, a novel error-resistant model for NTT is presented based on hybrid protection mechanisms, i.e., the use of hamming codes for detection and correction of errors in the twiddle factors and the use of parity computed for all NTT coefficients for error detection. Benchmarking error protection overheads on a Xilinx Virtex-7 FPGA reports 16.4% and 10.8% degradation on the hardware efficiency when the hamming codes for twiddle factors and parity bit for NTT coefficients are used to mitigate errors, respectively. A total of 29.2% area overhead is benchmarked when compared to the standard unprotected NTT implementations.

This research investigates efficient architectures for the implementation of the CRYSTALS-Dilithium post-quantum digital signature scheme on reconfigurable hardware, in terms of speed, memory usage, power consumption and resource utilisation. Post quantum digital signature schemes involve a significant computational effort, making efficient hardware accelerators an important contributor to future adoption of schemes. This is work in progress, comprising the establishment of a comprehensive test environment for operational profiling, and the investigation of the use of novel architectures to achieve optimal performance.

The latest research indicates that quantum computers will be realized in the near future. In theory, the computation speed of a quantum computer is much faster than current computers, which will pose a serious threat to current cryptosystems. Post-quantum cryptography (PQC) is a class of cryptography based on underlying mathematical problems that are considered infeasible to crack even with access to a quantum computer. The supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol is a new post-quantum cryptosystem, which offers advantages in reduced secret key length and attack resistance. SIDH is the basis of the supersingular isogeny key encapsulation (SIKE) protocol, which is in the second round of the U.S. National Institute of Standards and Technology (NIST) PQC standardization process. In this article, we propose a new modular multiplication algorithm and a new interleaved hardware architecture for SIDH. Performance results for the proposed modular multiplier using four parameter sets for the prime, p that correspond to the SIKE Round 2 parameter sets show significant advantages in speed.

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, one of the leading candidates for post-quantum security, relies heavily on discrete Gaussian samplers to provide necessary uncertainty, obfuscating computations on secret information. For reconfigurable hardware, the cumulative distribution table (CDT) scheme has previously been shown to achieve the highest throughput and the smallest resource utilisation, easily outperforming other existing samplers. However, the CDT sampler does not scale well. In fact, for large parameters, the lookup tables required are far too large to be practically implemented. This research proposes a hierarchy of multiple smaller samplers, extending the Gaussian convolution lemma to compute optimal parameters, where the individual samplers require much smaller lookup tables. A large range of parameter sets, covering encryption, signatures, and key exchange are evaluated. Hardware-optimised parameters are formulated and a practical implementation on Xilinx Artix-7 FPGA device is realised. The proposed sampling designs demonstrate promising performance on reconfigurable hardware, even for large parameters, that were otherwise thought infeasible.

Lattice-based cryptography is one of the most promising branches of quantum resilient cryptography, offering versatility and efficiency. Discrete Gaussian samplers are a core building block in most, if not all, lattice-based cryptosystems, and optimised samplers are desirable both for high-speed and low-area applications. Due to the inherent structure of existing discrete Gaussian sampling methods, lattice-based cryptosystems are vulnerable to side-channel attacks, such as timing analysis. In this paper, the first comprehensive evaluation of discrete Gaussian samplers in hardware is presented, targeting FPGA devices. Novel optimised discrete Gaussian sampler hardware architectures are proposed for the main sampling techniques. An independent-time design of each of the samplers is presented, offering security against side-channel timing attacks, including the first proposed constant-time Bernoulli, Knuth-Yao, and discrete Ziggurat sampler hardware designs. For a balanced performance, the Cumulative Distribution Table (CDT) sampler is recommended, with the proposed hardware CDT design achieving a throughput of 59.4 million samples per second for encryption, utilising just 43 slices on a Virtex 6 FPGA and 16.3 million samples per second for signatures with 179 slices on a Spartan 6 device.

Lattice-based cryptography is a quantum-safe alternative to existing classical asymmetric cryptography, such as RSA and ECC, which may be vulnerable to future attacks in the event of the creation of a viable quantum computer. The efficiency of lattice-based cryptography has improved over recent years, but there has been relatively little investigation into hardware designs of digital signature schemes. In this paper, the first hardware design of the provably secure Ring-LWE digital signature scheme, Ring-TESLA, is presented, targeting a Xilinx Spartan-6 FPGA. The results better compactness of all previous lattice-based digital signature schemes in hardware, and can achieve between 104-785 signatures and 102-776 verifications per second.

Multipliers requiring large bit lengths have a major impact on the performance of many applications, such as cryptography, digital signal processing (DSP) and image processing. Novel, optimised designs of large integer multiplication are needed as previous approaches, such as schoolbook multiplication, may not be as feasible due to the large parameter sizes. Parameter bit lengths of up to millions of bits are required for use in cryptography, such as in lattice-based and fully homomorphic encryption (FHE) schemes. This paper presents a comparison of hardware architectures for large integer multiplication. Several multiplication methods and combinations thereof are analysed for suitability in hardware designs, targeting the FPGA platform. In particular, the first hardware architecture combining Karatsuba and Comba multiplication is proposed. Moreover, a hardware complexity analysis is conducted to give results independent of any particular FPGA platform. It is shown that hardware designs of combination multipliers, at a cost of additional hardware resource usage, can offer lower latency compared to individual multiplier designs. Indeed, the proposed novel combination hardware design of the Karatsuba-Comba multiplier offers lowest latency for integers greater than 512 bits. For large multiplicands, greater than 16,384 bits, the hardware complexity analysis indicates that the NTT-Karatsuba-Schoolbook combination is most suitable.

Lattice-based cryptography has gained credence recently as a replacement for current public-key cryptosystems, due to its quantum-resilience, versatility, and relatively low key sizes. To date, encryption based on the learning with errors (LWE) problem has only been investigated from an ideal lattice standpoint, due to its computation and size efficiencies. However, a thorough investigation of standard lattices in practice has yet to be considered. Standard lattices may be preferred to ideal lattices due to their stronger security assumptions and less restrictive parameter selection process.

As the development of a viable quantum computer nears, existing widely used public-key cryptosystems, such as RSA, will no longer be secure. Thus, significant effort is being invested into post-quantum cryptography (PQC). Lattice-based cryptography (LBC) is one such promising area of PQC, which offers versatile, efficient, and high performance security services. However, the vulnerabilities of these implementations against side-channel attacks (SCA) remain significantly understudied. Most, if not all, lattice-based cryptosystems require noise samples generated from a discrete Gaussian distribution, and a successful timing analysis attack can render the whole cryptosystem broken, making the discrete Gaussian sampler the most vulnerable module to SCA. This research proposes countermeasures against timing information leakage with FPGA-based designs of the CDT-based discrete Gaussian samplers with constant response time, targeting encryption and signature scheme parameters. The proposed designs are compared against the state-of-the-art and are shown to significantly outperform existing implementations. For encryption, the proposed sampler is 9× faster in comparison to the only other existing time-independent CDT sampler design. For signatures, the first time-independent CDT sampler in hardware is proposed.

Large integer multiplication is a major performance bottleneck in fully homomorphic encryption (FHE) schemes over the integers. In this paper two optimised multiplier architectures for large integer multiplication are proposed. The first of these is a low-latency hardware architecture of an integer-FFT multiplier. Secondly, the use of low Hamming weight (LHW) parameters is applied to create a novel hardware architecture for large integer multiplication in integer-based FHE schemes. The proposed architectures are implemented, verified and compared on the Xilinx Virtex-7 FPGA platform. Finally, the proposed implementations are employed to evaluate the large multiplication in the encryption step of FHE over the integers. The analysis shows a speed improvement factor of up to 26.2 for the low-latency design compared to the corresponding original integer-based FHE software implementation. When the proposed LHW architecture is combined with the low-latency integer-FFT accelerator to evaluate a single FHE encryption operation, the performance results show that a speed improvement by a factor of approximately 130 is possible.

Cloud computing technology has rapidly evolved over the last decade, offering an alternative way to store and work with large amounts of data. However data security remains an important issue particularly when using a public cloud service provider. The recent area of homomorphic cryptography allows computation on encrypted data, which would allow users to ensure data privacy on the cloud and increase the potential market for cloud computing. A significant amount of research on homomorphic cryptography appeared in the literature over the last few years; yet the performance of existing implementations of encryption schemes remains unsuitable for real time applications. One way this limitation is being addressed is through the use of graphics processing units (GPUs) and field programmable gate arrays (FPGAs) for implementations of homomorphic encryption schemes. This review presents the current state of the art in this promising new area of research and highlights the interesting remaining open problems.