Efficient computing of n-dimensional simultaneous Diophantine approximation problems

In this paper we consider two algorithmic problems of simultaneous Diophantine approximations. The first algorithm produces a full solution set for approximating an irrational number with rationals with common denominators from a given interval. The second one aims at finding as many simultaneous solutions as possible in a given time unit. All the presented algorithms are implemented, tested and the PariGP version made publicly available

Numerical computing of extremely large values of the Riemann-Siegel Z-function

A PhD értekezés egy olyan hatékony algoritmust mutat be, amely a Riemann-Siegel Z-függvény kiugró értékeinek meghatározására szolgál. A Riemann-féle zeta függvény nagyon fontos szerepet játszik a matematika és a fizika különböző területein. A zeta függvény kritikus egyenesen elhelyezkedő nagy értékeinek meghatározása hozzásegíthet minket a prímszámok eloszlásának sokkal jobb megértéséhez. A doktori értekezés első részében egy olyan algoritmust készítettünk, amelynek segítségével gyorsan és hatékonyan tudjuk a Riemann-Siegel-Z függvényben szereplő többváltozós függvényt közelíteni nagyon sok n egészre. Módszerünk többdimenziós szimultán Diofantikus egyenletek approximációján alapul, melynek megoldására hatékony algoritmust mutattunk be (MAFRA algoritmus). Ezt az algoritmust felhasználva kidolgoztunk egy új algoritmust (RS-PEAK), amelynek segítségével gyorsan és hatékonyan lehet meghatározni a Riemann-féle zeta függvény kritikus egyenesen elhelyezkedő kiugró értékeit. Az RS-PEAK algoritmus segítségével az MTA SZTAKI Desktop GRID hálózatát felhasználva sikerült nagyon nagy Z(t) értékeket publikálni, köztük a ma ismert legnagyobbat is, ahol t=310678833629083965667540576593682.05-ra a Z(t) =16874.202 értéket kapjuk. A disszertáció írásának időpontjában ez a legnagyobb publikált Z(t) érték. A doktori értekezésben több a Z(t) értékhez kapcsolódó számítási rekordot publikáltunk

The FormAI Dataset: Generative AI in Software Security Through the Lens of Formal Verification

This paper presents the FormAI dataset, a large collection of 112, 000 AI-generated compilable and independent C programs with vulnerability classification. We introduce a dynamic zero-shot prompting technique constructed to spawn diverse programs utilizing Large Language Models (LLMs). The dataset is generated by GPT-3.5-turbo and comprises programs with varying levels of complexity. Some programs handle complicated tasks like network management, table games, or encryption, while others deal with simpler tasks like string manipulation. Every program is labeled with the vulnerabilities found within the source code, indicating the type, line number, and vulnerable function name. This is accomplished by employing a formal verification method using the Efficient SMT-based Bounded Model Checker (ESBMC), which uses model checking, abstract interpretation, constraint programming, and satisfiability modulo theories to reason over safety/security properties in programs. This approach definitively detects vulnerabilities and offers a formal model known as a counterexample, thus eliminating the possibility of generating false positive reports. We have associated the identified vulnerabilities with Common Weakness Enumeration (CWE) numbers. We make the source code available for the 112, 000 programs, accompanied by a separate file containing the vulnerabilities detected in each program, making the dataset ideal for training LLMs and machine learning algorithms. Our study unveiled that according to ESBMC, 51.24% of the programs generated by GPT-3.5 contained vulnerabilities, thereby presenting considerable risks to software safety and security.Comment: https://github.com/FormAI-Datase

Statistical analysis of DH1 cryptosystem

In this paper we shall use some standard statistical methods to test the avalanche effect of a previously introduced cryptosystem based on automata compositions, called DH1 cryptosystem. We have generated sample data of encryption and decryption. In our first set of analysis we simply estimated the probabilities of the atoms of the discrete distribution separately in order to compare them with those of the binomial test distribution. In the second statistical analysis, we turned to a goodness-of-fit test. For this we used the χ2-test. Thirdly, we assumed that the sample comes from a binomial distribution and we calculated the maximum likelihood estimation of the two parameters. Finally we discuss some well-known further tests on randomness and related results. Our main conclusions based on the statistics all confirm that the avalanche effect is fulfilled

Edge Learning for 6G-enabled Internet of Things: A Comprehensive Survey of Vulnerabilities, Datasets, and Defenses

The ongoing deployment of the fifth generation (5G) wireless networks constantly reveals limitations concerning its original concept as a key driver of Internet of Everything (IoE) applications. These 5G challenges are behind worldwide efforts to enable future networks, such as sixth generation (6G) networks, to efficiently support sophisticated applications ranging from autonomous driving capabilities to the Metaverse. Edge learning is a new and powerful approach to training models across distributed clients while protecting the privacy of their data. This approach is expected to be embedded within future network infrastructures, including 6G, to solve challenging problems such as resource management and behavior prediction. This survey article provides a holistic review of the most recent research focused on edge learning vulnerabilities and defenses for 6G-enabled IoT. We summarize the existing surveys on machine learning for 6G IoT security and machine learning-associated threats in three different learning modes: centralized, federated, and distributed. Then, we provide an overview of enabling emerging technologies for 6G IoT intelligence. Moreover, we provide a holistic survey of existing research on attacks against machine learning and classify threat models into eight categories, including backdoor attacks, adversarial examples, combined attacks, poisoning attacks, Sybil attacks, byzantine attacks, inference attacks, and dropping attacks. In addition, we provide a comprehensive and detailed taxonomy and a side-by-side comparison of the state-of-the-art defense methods against edge learning vulnerabilities. Finally, as new attacks and defense technologies are realized, new research and future overall prospects for 6G-enabled IoT are discussed