Imagine: You are sitting in a coffee shop on your phone when all of a sudden you get the urge to check the balance of your bank account. You go to settings in your phone and connect to the free WiFi at the coffee shop. Then you goon the bank’s website or in their app and GAME OVER. Well, it would be if not for cryptography.

There are two forms of cryptography, public and private. Both help in internet security and keep other people from getting your information. It would be possible to go online without this technology, however, why would you? If there was no way to secure data and communication across the internet, no one would want to go on it. Since the beginning of human communication, humans have always wanted privacy. There are many things people do not want blurted out so the whole world knows. Privacy is a human right and their data and communication should be protected as such.

In this presentation, I will explore the two different methods of cryptography and give examples of each. These two methods need to be used in unison because private cryptography, although fast, is not secure. Public key cryptography is secure, but extremely slow. I will compare two examples of public key cryptography, explaining how it is evolving. Although still slow, cyber security experts have shortened the key length, making one form of public key faster than the other.

Great presentation, I wish we could have heard it in person. I really liked your abstract, plus the history behind cryptography I found fascinating. I did have a question about one of the “problems” brought up; it mentioned how the RSA Algorithm isn’t completely private because it would take much too long to accomplish anything. When was this a problem? ie have computers developed so much since then that it wouldn’t be a problem anymore? Nice job!

The RSA Algorithm is not private key cryptography because of the keys. Private key cryptography involves two identical keys that both the sender and receiver have. It is a form of public key cryptography because the public key is known to everyone, whereas the private key is only known to the receiver. Therefore, there are two different keys, they are not identical. With that being said, public key cryptography takes a very long time to complete. This is because the keys are longer than those in private key cryptography. In the example of the Caesar Cipher (an example of private key cryptography) I spoke of, the key was three bits long (because that is how far each letter was moved over by). In the RSA algorithm (an example of public key cryptography) the keys can be of varying lengths. The most popular today is 2048 bits. This means the key is 2048 long. This is a very large key, so it takes more time to encrypt and decrypt the data it is trying to protect. Elliptic curve cryptography (another example of public key cryptography) is a faster method. This is because a 256 bit key in elliptic curve cryptography is as secure as a 2048 bit key in the RSA Algorithm. Length of keys in public key cryptography has always been a problem. Elliptic curve cryptography is the cyber security experts’ way of trying to shorten the key so the process becomes quicker. It still takes a while but it takes less time than elliptic curve and it is just as safe. I hope this helped explain it better for you. Please let me know if you have anymore questions.

Excellent job with a very interesting and difficult topic! I have a good amount of experience with cryptography (I took the upper level Web Development course at Canisius) and never quite got the breadth of understanding to the topic as you illustrated here. Since i learned it in the computer science department, I never really got to see how abstract algebra plays a role in it, and you explained it very well! I really liked how you pulled in discussions on Fields and Abelian groups because it does show that something that was once thought of as purely theoretical, can later be found to be incredibly applicable. You did a really good job of giving both a breadth of knowledge on the subject while also going into the specifics just enough to help the reader learn what is really going on mathematically. What a way to finish the math major!

Hackers beware! Mathematics is here to protect your data! Very well done presentation! I liked the part where a professor printed off all of the passwords just so that he could have more time to work on his research. It is scary to think that high school students were able to crash computers back before all of this cryptography. I like how you slowly evolved from simple ciphers to more complex ciphers. I built a Caesar cipher machine in computer science and it was pretty easy so I now understand why it is so easy to decipher. I really like how you didn’t say that public keys or private keys were better. Rather, the optimal encryption is a blend of the two keys. I have never heard of the elliptic curve as a secure method for cryptography and I think that you did a great job explaining such a concept. Well done and I’m glad that you did not encrypt this whole presentation with a Caesar cipher although that would be an interesting project if you were looking for something to do on a rainy day!

Hello! I thought your presentation was excellent! I am completely new to cryptography, so I really appreciated all of the background information you gave to explain what cryptography is and why it is so important. You explained things in a way so that even someone completely unfamiliar to cryptography was still able to follow. Also, I think it’s amazing that you were able to cover so much information in one presentation! It’s very obvious that you are incredibly knowledgeable about this topic, and that you put in a significant amount of work to get this presentation to be so impressive. Also, I wanted to commend you on your abstract. Talk about attention-grabbing! I’m sorry you didn’t get to present this in person, but trust me when I say that everyone who reads it will know and appreciate all of your hard work! Great job!

Now many devices and users are connected with internet. In this meaning, cryptography is important role for protecting our data. Your introduction is really attracting because I think many people do not care too much about using free Wi-Fi at the coffee shop even if they tapped “I agree” when the message about possibility of insecure connection showed up before using Wi-Fi. Public and private keys are interesting concepts. I think they are also used at block chain.

I thoroughly enjoyed this presentation! Really well done on a complex topic. I know almost nothing about cryptography, so this was a good lesson for me personally. I always love learning about new avenues where math is essential. I also think this topic will be really useful in potential job opportunities as this is such an impressive subject to learn about. Great job Danielle, you should be really proud!

Definitely show a strong knowledge of the subject. As always I can tell you payed a lot of attention to the formatting and layout of the presentation. I’ve noticed that cryptography is just one of those topics that needs to be set up in a logical and systematic order or it will just confuse everyone and make the presentation go off course but this hit the nail on the head. Very good all around.

Great job! Cryptography is one of the most interesting fields of mathematics and public key encryption is perhaps one of the most useful things human beings have ever created. I’m always intrigued when I get to hear about this stuff, but it’s usually quite confusing. You did a good job of gradually increasing the complexity as the presentation went on, so we didn’t get lost.

Neat discussion on cryptography; I’m currently in the midst of developing a new website and chest-deep in hashing and encryption to maintain user security, thankfully, most of the difficult RSA stuff is done in the background with certificate signing authorities. It’s very neat to see what is going on behind the scenes with these algorithms! I had never heard about an alternative method to encryption involving elliptic curves!

Good work!