Cryptography Mathematics & Economics Term Paper Essay

Topic can be chosen by yourself. The subject is cryptography. It should be written around mathematics. For specific requirements, see the document.

Mathematics 348 Introduction to Cryptography Spring 2020

Final Term Paper Details There is no final exam in Spring 2020 Mathematics 348:02.

In lieu of an exam there will be a final term paper  The paper should be about 10-12 pages double-spaced, including a bibliography. This should be around 2000 words or more. The paper will contain your clear discussion of a topic in cryptography that you have researched. A list of possible projects is given below. You can also propose your own topic. Email me with your topic when you have chosen it. (at most two students will be doing the same topic). Make sure that you have the requisite background knowledge to complete the project - for example, if the project requires knowledge of physics to carry out you should have that knowledge before beginning the project. Your paper should be a double-spaced typewritten document, which will be submitted online as a PDF file. Follow accepted form for a term paper, writing in complete sentences, providing citations to references and a bibliography at the end of the paper. A large part of your paper might be mathematical in nature. In this case, you will probably want to include formulas and short derivations/ideas. (Longer proofs do not belong in a piece of exposition but you may want to cite a resource which contains them.) The typical way to include formulas in typewritten works is to use a program like LATEX, but LATEX has a steep learning curve. Handwritten formulas and formulas typeset using Microsoft Word or similar will also be accepted. (The bulk of the paper should still be typewritten, however.) The project must consist of your own work. Plagiarism will be reported to the Office of Student Conduct and could lead to automatic failure of the course. When in doubt, cite your materials. The goal of this term paper assignment is to analyze a topic in detail and to provide an exposition of the topic accessible to others. Some introduction to topics is in our text, but you will have to use several other sources as well for your paper. Grades for the paper will involve the following criteria: General standards as a term paper: Is your paper accurately cited, does it match the formatting guidelines, and is it your own work? Overall quality of exposition: Has an effort been made to make your paper accessible to the reader? Does it give enough background and is it edited well? Overall quality of analysis: A good paper should cover explanations in addition to facts. Does the paper address the why in addition to the what? Don’t just state things. Explain why they are true. Quality of technical writing: Are the mathematical sections in your paper clear, convincing, and correct? Are sufficient details provided for the reader to appreciate the mathematics? SUGGESTED FINAL TERM PAPER TOPICS You are free to suggest your own topic, or to choose one in the list below or suggested by it. Send me email when you’ve decided on a paper topic so it can be reserved (at most two students can have the same topic) 1. Index calculus for discrete logarithm problems in groups coming from elliptic curves 2. Secret Sharing. Is it possible to subdivide a piece of secret information in such a way that a certain threshold of cooperation is required to reassemble the secret? 3. Zero knowledge proofs. Is it possible to prove that you possess some knowledge without giving your verifier any further information? Can this be applied? 4. Cryptographic aspects of blockchains and bitcoins. Cryptocurrencies such as Bitcoin rely on the security of a blockchain to verify transactions. What cryptography does the blockchain use? 5. Polynomial time tests to determine if an integer N is prime 6. Cryptanalysis and Quantum Computers. Quantum computers (if they can be built to scale) could run algorithms that factor large integers and compute discrete logarithms in polynomial time. How do these algorithms work? What effect would their introduction have on modern cryptography? 7. Collision Attacks on Hash Functions. Recently, the security of many common hash functions (e.g. SHA-0 and MD5) were called into questions after “collisions” were found in them. What are the implications of these findings? 8. Fully Homomorphic Encryption. What are the goals of fully homomorphic encryption and what is state-of-the-art in this pursuit? What is the connection to cloud computing? 9. Attacks on RSA public key encryption (Wiener’s low decryptor exponent attack,etc.) 10. Lattice-Based Cryptography. What is the underlying ‘hard’ problem used in latticebased cryptography? What are the potential advantages to lattice-based cryptography over discrete log or factorization-based cryptography? 11. The General Number Field Sieve. What is the history of the general number field sieve (GNFS)? What’s the difference between the quadratic sieve into the GNFS? Why do we expect the GNFS to be faster? 12. The Enigma Cipher. The Allied crack of the German Enigma encryption scheme is credited with shortening the length of World War II by a considerable amount. How did Enigma work? How was it cracked? What was the role of computers in this process? 13. Commonly-Used Protocols. How do commonly-used encryption protocols (e.g. AES or SSL) work? What separates them from some of the protocols we’ve studied in class? 14. The History of Factoring Algorithms. Which factoring algorithms have set records for integer factorization? How has their development evolved? 15. Side Channel Attacks. What is a side-channel attack? How have metrics like power consumption and processing time been used to crack cryptosystems? 16. Pseudo-random Number Generation. How are random numbers generated in practice? What are random numbers used for and how can we make numbers in a determinis- tic way which behave randomly? Alternatively, discuss the NIST standard random number generator and allegations that it contains an NSA-designed backdoor. 17. Encrypted voting protocols. The different goals we wish voting protocols to achieve, including accuracy, privacy, and freedom from coercion, and various cryptographic, as well as paper based (and combinations thereof) ways to achieve them. Cryptography of Voting Machines. What sort of cryptographic protocol could be implemented to prove to voters that their votes have been correctly recorded? Can this be done in a way which doesn’t release ‘receipts’ which could incentivize vote-selling? Security problems of Diebold voting machines. 18. Secure messaging systems. What cryptographic techniques do whatsapp or OTR use and how good is it? 19. Security/insecurity of wireless computing, especially the “Bluetooth” and 802.11 WiFi protocols 20. Cryptanalysis Based on Weak PRNG. How does weak pseudo-random number generation compromise cryptographic protocols like RSA key generation? 21. Modern symmetric cryptosystems 22. The Crypto Wars. Government use of cryptography was ‘complicated’ by the emergence of strong cryptography in the public sector. How did the U.S. government react to the rise of public sector cryptography? How have the governments of other countries acted to suppress the use of strong cryptography? 23. History of factoring and prime proving methods. Current status of size of general numbers which can be factored in reasonable time. 24. The Texas Instruments Signing Key Controversy. In 2009, Benjamin Moody published the factors of the 512-bit RSA key used to sign the TI-83+ series graphic calculator. How was this accomplished, and what does this say about the rise of computing power in the last few decades? What was the response of Texas Instruments? 25. Most factorization-based cryptographic protocols begin by choosing two primes, p and q, and forming N = pq. Beyond overall largeness, what must be true of p and q to guarantee cryptographic security? Will a ‘random’ large prime work for cryptography, or are strong primes relatively rare?