Detection of soft errors and faults are one of the most critical factors in ensuring the reliability of algorithm implementations. Multiplication, as a fundamental and computationally intensive operation, is particularly vulnerable to such errors. Given its widespread use in cryptography and coding applications, detecting these errors is crucial. For example, in hash functions, even a single-bit change in the input can completely alter the output (ideally, each bit of the output changes with a probability of 12). Montgomery multiplication as an efficient multiplication method is an integral part of numerous cryptographic applications expanding both classical and post quantum cryptography. For that reason, this paper introduces a fault detection method for the multiple-precision Montgomery modular multiplication algorithm based on partial recomputation. Through extensive simulations and implementations, we demonstrate that our approach efficiently detects both permanent and transient errors with a high success rate, while imposing modest area and time overhead on the system.

Addressing the looming threat posed by quantum computers capable of breaching current public key cryptography schemes has become imperative. To this end, the National Institute of Standards and Technology (NIST) initiated a competition in Post-Quantum Cryptography, resulting in the selection of four schemes as the new standardized replacements, while a fourth round and an additional signature round is still ongoing. Notably, CRYSTALS-Dilithium, a lattice-based signature scheme, has exhibited promising resilience due to its efficiency and simplicity. Despite the finalization of standardization for these new four schemes, transitioning from classical cryptography to these alternatives necessitates further investigation and analysis. Comprehensive scrutiny of these newly standardized schemes is imperative, including considerations of implementation efficiency across various platforms and side-channel vulnerability analysis. This article introduces a novel design leveraging physical unclonable functions to bolster the physical security of CRYSTALS-Dilithium. Physical security is paramount in scenarios where network nodes are exposed to public scrutiny, potentially making them targets for adversaries. After discussing the advantages of our design compared to the original design, we implemented it on two different architectures, ARMv7 and ARMv8. Our results indicate substantial improvements in both security and performance compared to existing references. Moreover, noting the new competition initiated by the NIST in 2023 for new signatures (first round finalized in October 2024), potentially the proposed schemes can be adopted to the new standards set to be finalized in the coming years. These make our scheme not solely confined to the current standards and would be an important merit of the presented approaches.

Polynomial multiplication stands out as a highly demanding arithmetic process in the development of post-quantum cryptosystems. The importance of the number-theoretic transform (NTT) extends beyond post-quantum cryptosystems, proving valuable in enhancing existing security protocols such as digital signature schemes and hash functions. CRYSTALS-KYBER stands out as the sole public key encryption (PKE) algorithm chosen by the National Institute of Standards and Technology (NIST) in its third round selection, making it highly regarded as a leading post-quantum cryptography (PQC) solution. Faults have the potential to disrupt cryptographic systems, compromise data integrity, and enable side-channel attacks, making the incorporation of robust error detection mechanisms essential. This article introduces algorithm-level fault detection schemes in the NTT multiplication using Negative Wrapped Convolution ( NWC ) and the NTT tailored for Kyber Round 3, representing a significant enhancement compared with previous research. We evaluate this through the simulation of a fault model, ensuring that the conducted assessments accurately mirror the obtained results. Our fault detection scheme is designed to address both malicious fault injection attacks on Kyber and naturally occurring faults. Furthermore, we assessed the effectiveness of the proposed error detection scheme for the NTT implemented in both NWC and Kyber , using AMD/Xilinx Artix-7 FPGA, HLS and processor-based approaches. In our FPGA implementation of NWC , the integration of our error detection approach achieves near-100% fault coverage with minimal area overhead and results in only a 12% increase in latency compared with the original hardware design. Finally, we attained an error detection ratio of nearly 100% for the NTT operation in Kyber , with a clock cycle overhead of 16% on the Cortex-A72 processor.

The Z-transform is a fundamental and strong tool being widely utilized in signal processing and various other applications such as communications and networking. By analyzing the Z-transform of a signal, one can extract critical information about its stability, causality, frequency response, energy and power, and overall behavior of the signal. However, errors caused either by environmental changes or malicious injections in large-scale integration (VLSI) implementations can critically compromise the integrity and reliability of its output. Failure to detect such faults may result in unpredictable, erroneous, and misleading function analyses. Therefore, the ability to detect soft errors and faults before accepting the results is of paramount importance. In this article, we propose an efficient fault detection method that combines algorithmic-level checks with partial recomputation to identify both transient and permanent faults with a high error coverage rate across various injection scenarios. The AMD/Xilinx field-programmable gate array (FPGA) implementation of our design demonstrated only a modest increase in time and area overhead. To the best of our knowledge, fault detection for the Z-transform function has not been previously studied.

It is well-studied that quantum computing breaks the security of the current worldwide implemented public key cryptosystems. This forces us toward post quantum cryptography (PQC) whose security remains solid even against adversaries having access to quantum computers. For this matter, National Institute of Standards and Technology (NIST) announced four winners in 2022. Among them, CRYSTALS-Kyber which is the only KEM/PKE algorithm, is the aim of this paper. In this paper, through using physical unclonable functions (PUF) and true random number generators (TRNG), we improve the overall security of Kyber and provide physical security to it. Our implementation results on ARMv7 and ARMv8 architectures, indicate significant speedup, compared to the reference work. For example, for the CCA.KEM-KeyGen() algorithm, we achieved roughly 26%, 13%, and 10% speedup at security levels of 512, 768, and 1024 on ARMv7 implementation, and 25%, 12%, and 10% for ARMv8 implementation. Comparing the implementation results of our design with the reference work indicates that both the security and the system performance are improved.

Elliptic curve scalar multiplication (ECSM) stands as a crucial subblock in elliptic curve cryptography (ECC), which represents the most widely used prequantum public key cryptography. Hardware constructions of cryptographic systems utilizing ECSM have been subject to permanent or transient errors. In cryptographic systems, it is important to validate the correctness of the underlying computation performed on hardware or software to identify such errors. In this article, we present new fault detection schemes in window method scalar multiplication, which, to the best of our knowledge, has not been previously investigated. Our approach involves introducing refined algorithms and implementations that can effectively counter both permanent and transient errors. We assess this by simulating a fault model, ensuring that the evaluations conducted reflect the obtained results. As a result, we achieve a significantly extensive coverage of errors. Finally, we benchmark our proposed error detection scheme on ARMv8 and field-programmable gate array (FPGA) to demonstrate the implementation and resource overhead. On Cortex-A72 processors, we maintain a clock cycle overhead of under 3%. In addition, when implementing our error detection method on different FPGAs, including Zynq Ultrascale+, Artix-7, and Kintex Ultrascale+, we achieve comparable throughput while introducing a mere 2% increase in area compared with the original hardware implementations.

Elliptic curve scalar multiplication (ECSM) is a fundamental element of public key cryptography. The ECSM implementations on deeply embedded architectures and Internet-of-nano-Things have been vulnerable to both permanent and transient errors, as well as fault attacks. Consequently, error detection is crucial. In this work, we present a novel algorithm-level error detection scheme on Montgomery Ladder often used for a number of elliptic curves featuring highly efficient point arithmetic, known as Montgomery curves. Our error detection simulations achieve high error coverage on loop abort and scalar bit flipping fault model using binary tree data structure. Assuming n is the size of the private key, the overhead of our error detection scheme is$O(n)$. Finally, we conduct a benchmark of our proposed error detection scheme on both ARMv8 and field-programmable gate array (FPGA) platforms to illustrate the implementation and resource utilization. Deployed on Cortex-A72 processors, our proposed error detection scheme maintains a clock cycle overhead of less than 5.2%. In addition, integrating our error detection approach into FPGAs, including AMD/Xilinx Zynq Ultrascale+ and Artix Ultrascale+, results in a comparable throughput and less than 2% increase in area compared with the original hardware implementation. We note that we envision using adoptions of the proposed architectures in the postquantum cryptography (PQC) based on elliptic curves.