The Building Blocks of Cryptography: Numbers and Operations

We all use numbers daily, often without thinking about it. We count objects with positive integers like 1, 2, 3, and split the bill at a restaurant, which might give us a decimal amount like $5.35 per person. When our investments lose value, we might see profit/loss percentage as -3.5%.

At its core, a number is just a way to represent quantity. What makes numbers truly useful is the fact that we can perform actions, or "operations" on them. For instance, with addition, we can combine numbers: 3 + 4 = 7 or (-3) + (-4) = -7. Similarly, multiplication allows us to scale numbers: 3 * 4 = 12 or 1.1 * 3 = 3.3. These operations feel natural to us, so we don’t often stop to consider the rules behind them -- even though some of them might sound counter-intuitive like why multiplying two NEGATIVE numbers results in a POSITIVE number?

In this chapter, we'll start to explore how numbers and operations are two separate concepts but deeply connected. Let's dive in!