Ideally, a paper will include a mix of formal mathematical content and less formal discussion of the significance or conceptual background of the topic; the exact mix will depend on the topic. The intended audience of this papers is other students in math 341; in particular, papers should be written clearly enough that, after reading them, another student would understand the topic. Students are encouraged to exchange papers with each other for additional feedback.

Suggested topics (you can also come up with your own):

- AKS primality algorithm

This is the deterministic polynomial time algorithm for testing primality. Many expositions are focused on achieving optimal bounds, which makes them much harder to read. Unless you really want to dive into that (and have the background for it), the mathematical side of this paper should just present some version of this algorithm, ideally the simplest version, even if the bounds are worse. - Bitcoin

Some discussion of the bitcoin (or a similar cryptocurrency) protocol. This could go a number of directions-comparisons of different cryptocurrencies, a detailed discussion of how the bitcoin protocol works (probably less of the number theoretic details and more on questions about who gets information about what and what security commitments the algorithm is based on)

- Probabilistically Checkable Proofs

A discussion of what probabilistically checkable proofs are and how the math behind them works - Hashing

Hashing algorithms are an essential piece of many cryptographic algorithms which we've glossed over. This could focus on detailed discussion of some particular algorithm (like the common but deprecated MD5 or the still current SHA-2 and SHA-3), or on the use and deprecation of SHA-1 - Password security

The best practices for software and websites that use password authentication, like how password hashing and salting works. - Web security

How websites use cryptographic protocols to securely exchange private data over insecure networks. - Malware encryption

Some hackers have taken to using malware to encrypt files and then hold people and companies ransom to decrypt them. This is currently in the news because it happened to a hospital in LA with a ransom of a million dollars. - The Apple/FBI dispute over a backdoor

This is a big topic, but a paper should focus on the cryptographic aspects: why does the FBI need Apple's help getting data of an iPhone, and how are iPhones secured to make this difficult - Election security

Various schemes have been proposed to use cryptographic techniques to verify election results and limit election fraud. - Quantum computing

Perhaps covering the basics of quantum computing and Shor's algorithm (the quantum algorithm for quickly factoring integers)