This is the 2nd study notes post for the college linear algebra course. Here is the review of Purdue MA 26500 Spring 2023 midterm I. I provide solutions to all exam questions as well as concise explanations.
Linear algebra provides mathematical tools to represent and analyze data and models in higher dimensions. It is essential for machine learning, computer graphics, control theory, and other scientific and engineering fields. Starting from this post, I will provide study guides and solutions to Purdue MA26500 exams in the last few semesters.
This article first supplements two specific integer factorization methods - Fermat's factorization method and Pollard's rho algorithm, explaining the essence of their algorithms and applicable scenarios, and provides a Python reference implementation. Next, it analyzes in detail a classic low private exponent attack - Wiener's attack, elaborating on the mathematical basis, the attack principle, and the attack procedure, with a complete Python program. The article also cites the latest research paper proposing a new upper bound for the private exponent when Wiener's attack is successful and verifies the correctness of this limit with a test case.
In the history of mathematics, Pierre de Fermat was a special figure. His formal occupation was as a lawyer, but he was exceptionally fond of mathematics. Although an amateur, Fermat’s achievements in mathematics were no less than those of professional mathematicians of the same era. He contributed to modern calculus, analytic geometry, probability, and number theory. Especially in the field of number theory, Fermat was most interested and achieved the most outstanding results.
TLS (Transport Layer Security) is a cryptographic protocol to secure network communication. TLS 1.3 is the latest version of the TLS protocol, succeeding TLS 1.2. TLS 1.3 aims to provide more robust security, higher privacy protection, as well as better performance than previous versions. Here is a brief introduction to TLS 1.3. Also, we discuss NIST's requirement for TLS 1.3 readiness and give examples of enabling TLS 1.3 in some commonly used web servers.
RSA is a public-key cryptosystem built on top of an asymmetric encryption algorithm, which was jointly invented by three cryptographers and computer scientists at the Massachusetts Institute of Technology in 1977. The RSA public-key encryption algorithm and cryptosystem provide data confidentiality and signature verification functions widely used on the Internet. Since its birth, RSA has become a major research object of modern cryptography. Many cryptanalysts and information security experts have been studying its possible theoretical flaws and technical loopholes to ensure security and reliability in practical applications.
uClibc is a small and exquisite C standard library for embedded Linux systems. It is widely used in the development of low-end embedded systems and Internet of Things devices. Here are some recent experiences to provide convenience for engineers who need to solve similar problems or meet corresponding requirements.