mt-notes

a collection of notes concerning ML, math & programming


Designing an 8-Bit Integer Primality Test Using Logic Circuits

When working with digital circuits and number theory, I found that an interesting challenge is determining whether a given number is prime through purely combinational logic. Recently, I developed a circuit diagram for testing the primality of 8-bit integers using a Boolean function `f(a,b,c,d,e,f,g,h)`.

5 min read   ·   2024

Stack Overflow Vulnerabilities

This blog post explores the fundamentals of buffer overflows, including how they arise in C and C++ programs, the role of process memory layout and the x86/IA-32 architecture, and the significance of stack frames. It covers common overflow types — stack-based, off-by-one, BSS, and heap — and shows how attackers use techniques like NOP-sledding to gain elevated privileges. Finally, it illustrates how to craft a working exploit by injecting shellcode into a vulnerable application’s memory space.

76 min read   ·   2024

Solving Peg Solitaire with efficient Bit-Board Representations

Many of us might now the board game peg solitaire and might even have one of its many variants at home. Peg solitaire is a one-player game played on a board with n holes and n - 1 pegs. The number of holes depends on the board variant. For example, the English variant consists of 33 holes while the typical diamond variant consists of 41 holes. The rules of the game are rather easy.

74 min read   ·   2024

Deriving a Closed-Form Solution of the Fibonacci Sequence

The Fibonacci sequence might be one of the most famous sequences in the field of mathmatics and computer science. In this blog post we will derive an interesting closed-form solution to directly compute any arbitrary Fibonacci number without the necessity to obtain its predecessors first.

12 min read   ·   2024