Spring 2026
Math 75: Mathematical Cryptography
E-mail: salim.tayou@dartmouth.edu,
Office: Kemeny Hall 341.
Schedule:
- Meeting times:
- X-hour:
- Room:
- First/last meeting:
- Office hours: See Canvas for more details.
Syllabus:
Cryptography is the science of secure communication over an insecure channel. This course focuses on understanding how mathematics is used in the design of modern cryptosystems, including both theoretical and algorithmic aspects. Specific topics will vary, but may include: substitution ciphers and statistical inference, the Enigma machine and permutation groups, Diffie-Hellman key exchange and discrete logarithms, RSA and integer factorization, AES and finite fields, elliptic curve cryptography, homomorphic encryption and lattices, and quantum cryptography.
Recommended textbooks (not required):
- (HPS) Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman, An Introduction to Mathematical Cryptography, 2nd ed., 2014.
- (RS) Simon Rubinstein-Salzedo, Cryptography Links to an external site, 1st ed., 2018.
- (S) Simon Singh, The Code Book: The Science of Secrecy from Ancient Links to an external site.Egypt to Quantum Cryptography, 2000.
Prerequisites:
Math 71, or Math 25 and 31, or instructor permission. If you are unsure about your preparation, please talk to the instructor! See also Homework 0.
Grading:
- Homework will be assigned. The solutions must uploaded on Gradescope. Late homework can only be accepted under special circumstances. Collaborative work on homework is accepted but you must write your own solution as well as the names of the collaborators, see policy on Canvas for collaborative work on homework.
- The Final Grade will be based on homework (10%), two midterms (60%), and final exam (30%).
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Learning Outcomes:
By the end of this course, you should be able to:
- Understand how mathematics is used in modern cryptography;
- Solve mathematical problems: utilize abstraction and think creatively; and
- Use algorithms to solve computational problems..