### Week 1: Meet Alice, Bob, and Eve!

Hello everyone! As the first official week of my senior project has come to a close, I can say that alongside learning about exciting new concepts, I’ve already run into several challenges. To start off the week, I met with my wonderful on-site mentor, Dr. Ismert, and we discussed the basic premises of the BB84 protocol. BB84 protocol is a form of quantum key distribution, meaning that its goal is to securely share a secret key between two people, rather than distributing a secret message itself.

For example, say Alice sends Bob the message “run,” which she has encrypted to read “svo.” While the encrypted message may be shared over an unsecure channel, such as a phone call, the key that allows Bob to decode the message must be kept a secret. In this case, the “key” is to shift every letter in the word to the previous one in the alphabet (s—>r, v—>u, o—>n). Alice must find a way to tell Bob this secret key without someone else eavesdropping. This is where BB84 comes in by essentially allowing the receiving party to identify whether or not someone has been listening in during the exchange of the secret key.

Mathematically, BB84 replaces the letters with a string of “bits” (zeros and ones) and sends the secret key through “encoded photons.” These photons are encoded in one of two ways and must be measured with the correct one of these two methods in mind, or the data will be permanently scrambled. Dr. Ismert explained it to me as encoding a message into bouncy balls of different size and color. If Bob tries to measure the size of the bouncy ball when Alice has sent the message encrypted to be the color of the bouncy ball, he will get no information. If he correctly measures the color of the bouncy ball when Alice has sent the message as a color, Bob will receive the data. Similarly, if Eve has been listening into the conversation and attempted to measure photons, her actions will cause scrambled data if she chooses the wrong form of measurement, thereby notifying Bob and Alice that someone is listening in. Physically, to measure a property of a photon, a laser must be shot at the particle. If Eve listens to Alice’s call with Bob and attempts to take a measurement of the photon using a laser she will alter the photon’s state and scramble all data. Cool, right?

While this concept is incredibly interesting, I have found that understanding the math behind photons and “quantizing” information is incredibly nuanced, and I lack some background information. This is the first problem I have identified, and in the coming weeks I plan to take some online courses in linear algebra and introductory quantum mechanics to hopefully better grasp how quantum encryption works and to better relay what I’ve learned to all of you!

For the remainder of the week, I refreshed myself on RSA encryption which utilizes multiplication and factorization to encode data. The basic idea is that it’s relatively easy to multiply large numbers using a calculator. Finding the factors of HUGE numbers, on the other hand, is incredibly difficult. This is what makes RSA difficult to decode, but with stable quantum computers which can factor numbers much, much faster than classical computers can, RSA is no longer a secure method of encryption. Take a look at the picture below to see how RSA encryption works using the comparison of mixing paint colors. 🙂

This brings me to my second challenge: finding effective ways to describe the types of encryption I’m studying in an approachable manner. This week, I’ve attempted to use paint and bouncy balls to describe what I’ve been studying. I’m excited to receive any feedback you have as to what is effective and what isn’t, so I can improve my methods of explanation in the coming months. Finally, my faculty advisor, Mr. Smith, shared this amazing video with me which gives a great overview of the problems quantum computers raise and the revolution it has sparked amongst mathematicians in a race to solve these problems. I totally recommend checking it out to get more background on the goal of my project. The visual explanations are super sick too!

Thank you for tuning in, and I can’t wait to share more with you next week!

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