In preparation for a future post discussing Elliptic curve cryptography (ECC), I’d like to introduce the broader concept of public-key cryptography first. Though these concepts are general, I’ll use the RSA algorithm as an example of a public-key cryptography system. …

Recently, Bitcoin and other cryptocurrencies seem to be gaining a lot of attention. Bitcoin was the first to appear, and it has attracted economists, technologists, entrepreneurs, politicians, activists, libertarians, and the list goes on. Some people love it, and others seem to hate it. But why? Is Bitcoin real money…

A Non-Technical Guide to General Relativity and Black Holes — Last week we heard the news all over the internet. Elon Musk’s SpaceX conducted a test flight for the Mars starship in south Texas. Although the rocket exploded as it was landing, on Twitter, Elon deemed the test a success. They were able to collect crucial data for a future…

In this post, I want to show you a method to generate sorted permutations of a set. We will focus on generating these permutations in lexicographic or numeric order. There are several ways to do this, but some are better than others in terms of efficiency. We’ll also look at…

Combinatorics, Binomial Coefficients, and Pascal’s Triangle — Let’s take a taxicab ride through Manhattan in New York City. We’re starting from a point in the upper west side down to the lower east side. On this trip, we want to see as much of the city as possible. We want to see all the streets and avenues…

Most of us played with Lego blocks or jigsaw puzzles when we were kids–maybe you still do. You remember spending hours tinkering and rearranging them into different shapes and structures. Our imagination was the limit. These are very simple things: pieces of plastic and paperboard in a few different shapes…

It seemed easier in my mind when I first thought about it. But, finding a random prime number fast isn’t trivial. For example, the 5th prime number is 11, the 20th is 71. But, what about the 50th, 600th, or 20,000th prime number? I want to show you an efficient…

If you are a mobile or web application developer, it is likely that at some point you needed to add authorization and authentication to your applications. OAuth and OpenID Connect are security standards addressing these needs. OAuth takes care of authorization, while OpenID Connect, or OIDC, deals with authentication. Some…

Some may think routines are boring and that we should avoid them. But, they give us a sense of familiarity and control. They make us feel in control because they are predictable, and we know exactly what we need to do and what the outcome will be. …