Elliptic Curve Cryptography

By Noa Bearman, Kimberly Cruz Lopez, Tina Lin, Xintong Xiang, and Maria Neri Otero*

*Maria helped the group work through the problem set but was unfortunately unable to attend camp during the blog writing.

Introduction

Have you ever tried to send a secret message to a friend? Did it work? Was it secure? Well, one way to do so in a more secure way is by using Elliptic Curve Cryptography (ECC). Most people have never heard of ECC before, and two weeks ago, neither did we. However, in the past two weeks, we have been learning how to use this exciting application of the techniques of algebraic geometry and abstract algebra applied to the ancient art of keeping messages secure. ECC was first introduced by Victor Miller and Neal Koblitz in 1985. It was proposed as an alternative to other forms of cryptography with public-key systems such as DSA and RSA. Public-key systems involve the use of two different kinds of keys: a public key that is available to the public and a private key in which only the owner knows. The applications of ECC has been growing and has recently gained a lot of attention in industry and academia. The following information below will go more in-depth on what ECC is, how it works, its advantages, its disadvantages, and our progression throughout this course.

Knot Theory

By Nethania Okyere, Rachel Rozansky, Ashleigh Taylor, and Sylvia Towey

Knot Theory

The knot theory are two mathematical branches of topology. Its simply a loop in 3 dimensional space( doesn’t intersect itself). Knots can be described in various ways. Given a method of description, however, there may be more than one description that represents the same knot. For example, a common method of describing a knot is using a knot diagram. Any given knot can be drawn in many different ways using a knot diagram.

Mandelbrot Sets: the Magic of Math

By Tara Collins, Michelle Escobar, Kayla Rollins, and Logan White

When you hear the phrase computational dynamics, what comes to mind?

Images of glasses-clad tech whizzes staring into screens?
Flowcharts, oceans of coffee, and lightbulb moments?
Utter computer-related confusion?

The struggle of programming can be all too real.

Network Science

By Cameron Farrar, Elizabeth Gross, Shiropa Noor, and Rebecca Rozansky

Girls Talk Math was an eyeopening experience to a brand new world of mathematics. Over the past two weeks, we have been introduced to multiple topics and related professions. We learned about: quantum mechanics, surface classification, knot theory, computing & dynamics, elliptic curve cryptography, RSA encryption, special relativity and the most interesting of them all- NETWORK SCIENCE!

During our time at Girls Talk Math, we learned about the wonders of network science and graph theory. The difficult part of this otherwise enjoyable journey? Mathematica. Mathematica is a software created to make you suffer, especially if you already know computer science (AHEM BECKY). Basically, we created graphs, did calculations and got confused on Mathematica. Typing out all the commands took ages. We’ll show you some examples as we go through the different concepts we explored. Don’t worry- once you spend some time on Mathematica, you’ll get used to it.

Quantum Mechanics

By Kathryn Benedict, Olivia Fugikawa, Denna Huang, and Eleanor McAdon

Intro

Quantum mechanics is a subfield of physics. Like with any other major area of study, physics is divided into many smaller categories. Classical physics is the main one, which includes Newton’s Laws of Motion and basic principles of mechanics, like inertia and friction. Things get weird when you delve into modern physics, which includes special relativity, general relativity, and quantum mechanics. Special relativity deals with particles moving at the speed of light, general relativity works with incredibly massive objects and quantum mechanics is the physics of subatomic particles. This is what we worked on for the past two weeks and what our blog post is about!

RSA Encryption Cryptography

By Divya Aikat, Helena Harrison, Annie Qin, and Quinn Shanahan

The definition of cryptography is the art of writing and solving code. However, over the last two weeks, we learned so much more than just this textbook explanation. While working together within our team, we explored many different aspects behind cryptography. By building off our individual strengths, we prepared ourselves for higher level mathematics. The following is a synopsis of the progress we’ve made over the past two weeks.

Special Relativity

By Katie Clark, Tori Dunston, Kelly Fan, Abrianna Macklin, and McKenna Vernon

Picture a hummingbird. At any moment, it can go in any of the three dimensions it is a part of. So, it could go up and down, forwards and backwards, or left and right. But, one thing that is not taken into account is time. As it moves through space, it is also occupying time. However, we’re not used to thinking about our world in a four dimensional sense. But, as the movement of the pigeon progresses, so does time. This is known as the relationship between space and time, and it is the primary foundation that special relativity is built on. So, at any given moment, it actually can move in four dimensions at once. This can be simply modeled using a spacetime diagram.

Surfaces

By Elizabeth Datskevych, Nina Hadley, Sabrina James, and Rachel Ruff

In our problem set for the classification of surfaces, we learned many things about dimensions, folding, and the shapes folding makes. First we learned about what a dimension is. The definition of a dimension in this math is the direction an object can go. For example a bird can go up/down, left/right, and back/forth. Next we learned about folding and twisting objects. Diagram A shows a square with arrows on its side, which are the directions to fold. When you fold you match the arrows according to if they look-alike. So when you fold Diagram A it makes a cylinder. Now Diagram B has one arrow pointing the opposite of the other so you would twist before connecting the sides. Diagram B makes a Mobius band. We could make other shapes using the arrows such as the Klein bottle, and the torus. This topic was very fun and cool and it is a subject everyone will enjoy!!!!!!!!!!!!!!!!!!!!!!!#girlstalkmath #girlsrock #blog2017