Did you get the joke in the picture to the left? If not, you will do so in a few minutes. I was recently reading an article and I came across the terms mentioned in the title. From the looks of it, they are very close to each other, right? In many fields within mathematics, we talk … Continue reading Homomorphism vs Homeomorphism
Category: Mathematics
A Beginner’s Look At Lambda Calculus
Back in school, you must remember studying differential and integral calculus. Now what on earth is lambda calculus? Well, lambda calculus is basically a simple notation for functions and applications in mathematics and computer science. It has a significant impact in the field of programming language theory. It forms the basis for all the modern functional … Continue reading A Beginner’s Look At Lambda Calculus
Elliptic Curve Cryptography: Part 4/4 – How Do We Use Elliptic Curves?
In the previous blog post, we discussed about elliptic curves and saw what they look like. We also looked at some of their special properties that enable it to be a good trapdoor function. But this is still very mathematical, right? The curves are great to look at and we understand general concept of elliptic curves, but … Continue reading Elliptic Curve Cryptography: Part 4/4 – How Do We Use Elliptic Curves?
Elliptic Curve Cryptography: Part 3/4 – What Is An Elliptic Curve?
In the previous blog post, we discussed why RSA will not be sufficient anymore. We looked at how machines are getting stronger, and that we cannot rely on factorization as our primary mathematical foundation. We also talked a bit about what we are looking for in our new system, and then said a quick hello to … Continue reading Elliptic Curve Cryptography: Part 3/4 – What Is An Elliptic Curve?
Elliptic Curve Cryptography: Part 2/4 – Why Do We Need It?
In our previous blog post, we discussed public key cryptography and how it works in general. The RSA is so powerful because it comes with rigorous mathematical proofs of security. The authors basically proved that breaking the system is equivalent to solving a very difficult mathematical problem. When we say "difficult", what it means is … Continue reading Elliptic Curve Cryptography: Part 2/4 – Why Do We Need It?
Elliptic Curve Cryptography: Part 1/4 – Why Should We Talk About It?
Elliptic curve cryptography is one of the most powerful techniques used in the field of modern cryptography. Just to be clear, elliptic curves have nothing to do with ellipses. I agree that the name can be slightly misleading, but once we discuss what elliptic curves are, it will become much clearer. So as you may have … Continue reading Elliptic Curve Cryptography: Part 1/4 – Why Should We Talk About It?
What Is A Markov Chain?
If you have studied probability theory, then you must have heard Markov's name. When we study probability and statistics, we tend to deal with independent trials. What this means is that if you conduct an experiment a lot of times, we assume that the outcome of one trial doesn't influence the outcome of the next … Continue reading What Is A Markov Chain?
What Is Maximum Likelihood Estimation?
Let's say you are trying to estimate the height of a group of people somewhere. If the group is small enough, you can just measure all of them and be done with it. But in real life, the groups are pretty large and you cannot measure each and every person. So we end up having … Continue reading What Is Maximum Likelihood Estimation?
Dissecting The Riemann Zeta Function
The Riemann Zeta function is an extremely important function in mathematics and physics. It is intimately related to very deep results surrounding the prime numbers. Now why would we want to care about prime numbers? Well, the entire concept of web security is built around prime numbers. Most of the algorithms for banking security, cryptography, networking, … Continue reading Dissecting The Riemann Zeta Function
What Is A Singularity?
You must have heard the term "singularity" being used in various contexts. We see it in mathematics, physics, circuit design, mechanics, fluid dynamics, etc. The word "singular" means something that is extraordinary, unique, and strange. When we talk about singularity in mathematics, we usually refer to the uniqueness of mathematical objects. In particular, singularities refer … Continue reading What Is A Singularity?
