Significant advancements have been achieved in the field of quantum computing in recent years. If somebody ever creates a sufficiently strong quantum computer, many of the public-key cryptosystems in use today might be compromised. Kyber is a post-quantum encryption technique that depends on lattice problem hardness, and it was recently standardized. Despite extensive testing by the National Institute of Standards and Technology (NIST), new investigations have demonstrated the effectiveness of CRYSTALS-Kyber attacks and their applicability in non-controlled environments. We investigated CRYSTALS-Kyber’s susceptibility to side-channel attacks. In the reference implementation of Kyber512, additional functions can be compromised by employing the selected ciphertext. The implementation of the selected ciphertext allows the attacks to succeed. Real-time recovery of the entire secret key is possible for all assaults.

The subject matter of the article is pseudo-random number generators. Random numbers play the important role in cryptography. Using not secure pseudo-random number generators is a very common weakness. It is also a fundamental resource in science and engineering. There are algorithmically generated numbers that are similar to random distributions but are not random, called pseudo-random number generators. In many cases the tasks to be solved are based on the unpredictability of random numbers, which cannot be guaranteed in the case of pseudo-random number generators, true randomness is required. In such situations, we use real random number generators whose source of randomness is unpredictable random events. Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. The goal is to develop a mathematical model of the generator, which generates fast random numbers at a lower cost. At the same time, a high level of randomness is essential. Through quantum mechanics, we can obtain true numbers using the unpredictable behavior of a photon, which is the basis of many modern cryptographic protocols. It is essential to trust cryptographic random number generators to generate only true random numbers. This is why certification methods are needed which will check both the operation of the device and the quality of the random bits generated. The goal of the research is also to develop the model of a hybrid semi self-testing certification method for quantum random number generators (QRNG). The tasks to be solved are to create the mathematical model of a random number generator, which generates the fast random numbers at a lower cost. To create the mathematical model of a hybrid semi self-testing certification method for quantum random number generators. To integrate a hybrid semi self-testing certification method to the hybrid random number generator. the methods used are mathematical optimization and simulation. The following results were obtained: we present the improved hybrid quantum random number generator, which is based on QRNG, which uses the time of arrival of photons. The model of a hybrid semi self-testing certification method for quantum random number generators (QRNG) is offered in the paper. This method combines different types of certification approaches and is rather secure and efficient. Finally, the hybrid certification method is integrated into the model of the new quantum random number generator. Conclusions. The scientific novelty of the results obtained is as follows: 1. The hybrid quantum random number generator is offered, which is based on QRNG, which uses the time of the arrival of photons. It uses the simple version of the detectors with few requirements. The hybrid QRNG produces more than one random bit per the detection of each photon. It is rather efficient and has a high level of randomness. 2. The hybrid semi self-testing certification method for quantum random number generators (QRNG) is offered. The Self-testing, as well as device-independent quantum random number generation methods, are analyzed. The advantages and disadvantages of both methods are identified. Based on the result the hybrid method is offered. 3. The hybrid semi self-testing certification method for quantum random number generators is integrated into the offered model of the quantum random number generator. The paper analyzes its security and efficiency. The paper offers to use the new random number generator in the crypto-schemes.

The security of commonly used cryptographic systems like RSA and ECC might be threatened by the future development of quantum computing. Verkle-based HORST decreases the size of signatures by 75% (from 12.8 KB to 3.2 KB) and enables O(1)-sized proofs by replacing Merkle trees with Verkle trees. Because verification shifts from O(log t) to constant time, it is ideal for blockchain and IoT applications that require short signatures and fast validation. In order to increase efficiency, this study introduces Verkle-based HORST, a hash-based signature method that uses Verkle trees. Our primary contributions are the following: a formal security analysis proving maintained protection levels under standard assumptions; a thorough performance evaluation demonstrating significant improvements in signature size and verification complexity in comparison to conventional Merkle tree approaches; and a novel signature construction employing polynomial commitments to achieve compact proofs. The proposed approach has a lot of benefits for real-world implementation, especially when dealing with situations that call for a large number of signatures or settings with limited resources. We offer comprehensive implementation instructions and parameter choices to promote uptake while preserving hash-based cryptography’s quantum-resistant security features. Our findings suggest that this method is a good fit for post-quantum cryptography systems’ standardization.

Static analysis is a critical methodology for ensuring the quality, security, and safety of embedded, cyber-physical, and electronic software systems, particularly as such systems become increasingly complex and tightly coupled with hardware and real-time constraints. Through a systematic study of the literature, this paper summarizes the State-of-the-Art in static program analysis. We develop a comprehensive taxonomy of fundamental techniques, including model checking, abstract interpretation, data-flow analysis, and symbolic execution, and examine their application in modern analysis tools used in electronic and safety-critical systems. The survey thoroughly reviews applications across key domains, including vulnerability detection, automotive and embedded software verification, smart contract auditing, and AI-enabled electronic systems. We also critically analyze persistent challenges, including tool integration, scalability limitations, and the trade-off between analysis precision and soundness. Finally, by discussing emerging trends and future research directions—such as machine-learning-enhanced analysis and hybrid static–dynamic techniques—this work provides a structured framework to guide future research and industrial practice in the development of reliable electronic systems.

Symbolic execution of embedded systems faces path explosion, Satisfiability Modulo Theories (SMT) solver bottlenecks, interrupt nondeterminism, and environment modeling complexity. Recent artificial intelligence (AI)-guided approaches using reinforcement learning, graph neural networks, and large language models improve exploration efficiency, yet all reason over raw symbolic states and ignore structural equivalences that arise from symmetry in embedded software. This paper presents S³E, a formal framework that organizes symbolic execution around equivalence classes of states under symmetry transformations. Symmetry groups partition the state space into orbits, and exploration proceeds over canonical representatives within quotient transition systems. Symmetry-aware AI components operate on orbit representatives rather than raw states. Four theoretical results support the framework: orbit preservation, quotient soundness, canonicalization correctness, and constraint reuse correctness. An illustrative case study based on a FreeRTOS-like scheduling environment shows how symmetry reduction collapses equivalent states into orbits, with the potential for reductions that scale factorially with symmetric components. S³E is a theoretical framework; a toy-model prototype validates the core quotient-exploration and constraint-caching mechanis, while empirical evaluation on production firmware remains future work.

In recent years, work on quantum computers has made substantial progress. Many of the current public key cryptosystems can be broken if humans ever develop a powerful quantum computer. There are currently several commercial products that use these cryptosystems. Though we have developed defenses against quantum attacks, they are too risky and ineffective to be applied in daily life. The study analyzes hash-based digital signature methods. The evaluation of a digital signature using a Merkle tree. The paper investigates unique ideas using vector commitments and a Verkle tree. The authors of this study describe a novel, Verkle tree technology-based method for creating a digital signature system. This is accomplished using the Verkle tree, vector commitments, and vector commitments based on lattices for post-quantum aspects. This work also provides the theories behind post-quantum signature design using Verkle Tree.