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Section 3.4 Additional Resources

Please find the bibliography below. High praise is reserved for Tim McDevitt and Frank Arnold’s text [3.4.17], which is provided to the author’s students as a resource (and from which exercises are sometimes assigned as homework). Simon Singh’s The Code Book [3.4.20] is an excellent, richly detailed, and deeply readable source for the historical and sociopolitical context of cryptography as well as entertaining descriptions of the underlying mathematics. The Cipher Challenge at the back of the book leads students through all of the ciphers described therein; the author uses it as a way for students to earn extra credit by solving a set number of the ten parts. In order to emphasize the human aspects of cryptography and its contemporary relevance, one may have students watch a video or read about the NSA/GCHQ and other cryptographic agencies as well as their recent political activities. Given that the NSA is the United States’ largest employer of Ph.D. mathematicians, and in the context of the revelations of Edward Snowden and other recent whistleblowers, this discussion remains deeply relevant.

References References

[3]
  
Christensen, C. (2007). Polish Mathematicians Finding Patterns in Enigma Messages. Mathematics Magazine, 80(4), 247--223.
[4]
  
Christensen, C. (2009). Review of The Shadow Factory: The Ultra-Secret NSA from 9/11 to the Eavesdropping on America by James Bamford. Cryptologia, 33(4), 356--358.
[6]
  
Crisman, K.-D. (2021). Number Theory: In Context and Interactive.
[8]
  
Farhi, E., Gosset, D., Hassidim, A., Lutomirski, A., and Shor, P. (2010) Quantum Money from Knots. arXiv:1004.5127.
[12]
  
Johnston, E. (2006). Problems. Mathematics Magazine, 79(4), 311.
[13]
  
Karst, N. and Slegers, R. (2019). Cryptography in Context: Co-teaching Ethics and Mathematics. PRIMUS 29(9), 1039--1059.
[14]
  
Encryption: Last Week Tonight with John Oliver (HBO). (2016, March).
[15]
  
Marzuoli, A. and Palumbo, G. (2012). Fault-Tolerant Mosaic Encoding in Knot-Based Cryptography. arXiv:1206.5709
[16]
  
Marzuoli, A. and Palumbo, G. (2011). Post Quantum Cryptography from Mutant Prime Knots. International Journal of Geometric Methods in Modern Physics 8(7), 1571--1581.
[17]
  
McDevitt, T. and Arnold, F. (2012). Class Notes for Cryptologic Mathematics (FYS 100).
[18]
  
Reeds, J. (2006). John Dee and the Magic Tables in the Book of SOYGA. In John Dee: Interdisciplinary Studies in English Renaissance Thought, ed. S. Clucas. 177--204.
[20]
  
Singh, S. (2011). The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography.
[21]
  
Smith, A. and Whitcher, U. (2015). Making a Hash of Things. Math Horizons 23(2), 5--8.