Cryptography is the study of encrypting and decrypting messages in a way that keeps the information secure so that only the sender and receiver can understand the message. While there is a rich history of cryptography going back thousands of years, modern networks demand security on a level that was unimaginable even 50 years ago. We will focus on understanding the mathematics underlying many of the modern cryptosystems, including the symmetric key system AES and the public key systems RSA and Diffie-Hellman. In addition, we will also study digital signatures, hash functions, the applications to blockchains, such as Bitcoin and Ethereum, and the implications of quantum computing.

Given our experiences over the last two years, we should plan that to be flexible over the course of the semester when the unexpected arises. Let's all be kind to each other, and we'll figure it out.

I'm really excited for this class. This is going to be a really fun semester!

There are several primary objectives of any 200-level math course at Wheaton. By the end of this semester you should:

- Be able to formulate a concise, precise mathematical argument, including recognizing when it is complete or when further justification is needed
- Be able to read and communicate advanced technical concepts
- Be willing to approach a problem even if you do not know whether or not your approach will be successful. If it doesn't work out, try something else!
- Appreciate the necessity of rigorous mathematical arguments
- Continue in your development from being a consumer of mathematics to being a producer of mathematics

You should gain a deeper understanding of:

- How the security of modern communication depends on sophisticated mathematical concepts
- When a theoretic result gives a practical real-world solution, and when it does not
- The distinction between theoretic and practical security
- The advantages, and disadvantages, of symmetric and asymmetric encryption systems
- The mathematics underlying AES, RSA, Diffie-Hellman key exchange, Elgamal encryption, and DSA
- The reason for digital signatures and message authentication codes
- How the methods discussed this semester fit together in the TLS and blockchain protocols

Mathematics is a very active discipline that is best learned by doing rather than by observing. One of the features that makes your Wheaton education so special is that we have time in small classes to explore material together. The class meetings are not intended to be a complete encapsulation of the course material, but instead will focus on the major concepts from the Pre-Class Assignments and clarifying the more subtle ideas in the course.

You should expect to put in approximately 3 hours outside of class for each scheduled hour of class. In other words, expect to spend a roughly 9 hours per week on Cryptography outside of the scheduled class meetings. There will be some weeks where you spend more time, and there may be some weeks where you spend slightly less.

We operate under the Wheaton Honor Code for all of your academic work at Wheaton. This carries certain freedoms and responsibilities for both you as a student and me as a professor. I take this quite seriously.

Most likely, no Honor Code issues will arise this semester. If you are uncertain about whether a particular situation falls under the Honor Code, then please consult with me. However, if an Honor Code issue does come up, I will assume that you are prepared for the full consequences. Remember that you should write out, and sign, the following statement on all course work:

"I have abided by the Wheaton College Honor Code in this work."

Your final grade will be determined by

Pre-Class Assignments | 10% |

Class Engagement/Participation | 10% |

Problem Sets & Partner Evaluations | 30% |

Three Take-home Exams | 50% |

The purpose of reading the text, and watching the occasional assigned videos, before class is that if you are familiar with the basic concepts and definitions, then the class meetings can be devoted to the major ideas and subtleties of the material. Mathematical understanding is built in stages, and you will absorb the material more quickly if the class meetings are your second exposure to the fundamental ideas.

The Pre-Class Assignments are posted on the course webpage and include three or so questions that you should be able to answer after you have completed the reading and viewed any videos. You will submit your responses through onCourse.

I will grade the Pre-Class Assignments using a binary scale: If you make a serious attempt, you will get full credit, whether or not your answers are completely correct. The purpose of these questions is to encourage you to engage with the material before class. If you've read the text and watched any videos but don't understand how to answer a question, it is perfectly fine to say "I did the prep work but don't see how to approach this question." You'll definitely understand by the end of the end of the week!

Notice that the Pre-Class Assignments are due at 11:59 pm on Monday! This will give me enough time to review your responses before our class on Tuesday. You will be allowed to drop one Pre-Class assignment at the end of the semester.

A significant part of the class meetings will be devoted to working in small groups on problems that delve more deeply into the content introduced in the Pre-Class Assignments and discussed at the beginning of class. A substantial amount of your learning will happen during these collaborative sessions by bouncing ideas off of other students and seeing how other groups approach the problems. I will also determine your Engagement/Participation grade for each class meeting using a binary scale: You were present and engaged with your peers or you weren't.

However, I also know that there may be times when you have a valid reason for missing class. I'll be really flexible, so if you need to miss class, please let me know. Let's just keep the lines of communication open.

You will have a Problem Set due most Thursdays at 11:59 pm. I firmly believe that one of the best ways to build your understanding of mathematics is to explore the ideas with other students. Therefore, you will work on the Problem Sets in groups of two, or possibly three, and each group will turn in a single set of solutions. I will randomly assign new groups for every problem set. Depending on the timing around exams and breaks, a few of the Problem Sets may be individual assignments instead. There are more details about the logistics and expectations for your write-ups on the Guidelines for Problem Sets page.

The purpose of the exams is for you to demonstrate your understanding of the course material and, just as importantly, to give you feedback on where your understanding is strong and where you may need more work. The exams will be open-note take-home exams where you will have several days to work on them. See the Tentative Daily Syllabus for dates of the exams. I will provide more details about the structure of the exams as the time gets closer.

I know that exams can be stressful, especially with the other academic, extracurricular, and family commitments that you may have. To try to reduce some of this stress concerning your grade, I will weight your exam scores by differing amounts: Your lowest exam score will count 20% of your exam grade, the second lowest will count 30%, and the highest will count 50% of your exam grade. For example, if your four exam scores are 71, 82, and 93, then your overall exam average will be 85.3.

Please come see me during my drop-in office hours! No appointment necessary! If you have a conflict and cannot make my office hours, please email me and we can set up an appointment for another time.

Remember that the goal of the course is to help you learn Cryptography and develop your mathematical thinking! If there's any point where you feel that the structure of the class isn't working for you, please come by and we can figure out some possible strategies.

Wheaton is committed to ensuring equitable access to programs and services and to prohibit discrimination in the recruitment, admission, and education of students with disabilities. Individuals with disabilities requiring accommodations or information on accessibility should contact Accessibility Services at the Filene Center for Academic Advising and Career Services: accessibility@wheatoncollege.edu or (508) 286-8215.