This talk will discuss the history of linear feedback shift registers (LFSR) in cryptographic applications and will attempt to implement an algorithm in SAGE and Python to create a linear feedback shift register sequence (LFSR sequence) in cryptography. Also, this talk will describe an implementation of the Berlekamp-Massey Iterative Algorithm in SAGE and Python. This algorithm will be able to use the Linear Feedback Shift Register sequence generated by the first algorithm to find the sequence's connection polynomial. I will attempt to show that the connection polynomial of a given LFSR sequence is the reverse of a generator polynomial of the cyclic code of length p , where p is also the period of the LFSR sequence. This will provide a connection between cyclic error-correcting codes and LFSR sequences.
David Joyner, Department of Mathematics, United States Naval Academywdjoyner@gmail.com
"Linear Feedback Shift Registers and Cyclic Codes in SAGE,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 7
, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss2/7