Linear Feedback Shift Registers and Cyclic Codes in SAGE
Midshipman Timothy Brock
United States Naval Academy
Abstract: 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.
Advisor: Professor David Joyner, USNA Department of Mathematics