The Mathematical Foundations of Modern Cryptography: Exactness, Prime Numbers, and the Greatest Common Divisor
Welcome to the first post of this blog, dedicated to my academic journey in cryptography. The goal of this post is to introduce the fundamental mathematical concepts that guarantee the security of our digital communications. It is important to underline that the mathematics used in cryptography is profoundly different from what we apply in our daily routines. The absolute need for exactness In everyday life, the use of approximations is very common. For example, if a product costs $1.99, we naturally consider it as $2.00. However, in the field of modern cryptography, there is no tolerance for rounding errors. If a cryptographic algorithm approximates a value even by a microscopic fraction, the entire system fails. The digital "key" used to encrypt a message would no longer be able to decrypt it, making the information permanently inaccessible. For this reason, cryptography abandons decimal numbers and operates exclusively with integers (such as -1,...