Improving the Extended 10×10 Polybius Square Key Matrix for Playfair, Bifid, and Polybius Cipher

The Polybius Square is a cryptographic algorithm modified and enhanced over time to fit modern standards. A modification that is the focus of this study is the extension of the 5x5 Square Key Matrix into a 10x10 Square Key Matrix. This enhancement, however, has a glaring weakness, where using short keys would not give sufficient entropy to the extended key matrix, and the issue has not been thoroughly explored in most studies. This research proposes using the Linear Feedback Shift Register (LFSR) to solve this problem as a pseudo-random number generator using short keys to produce a more complicated key to create better entropy. The results show that the average avalanche effect of ciphers using the LFSR-enhanced 10x10 key matrix compared to ciphers that use an unmodified 10x10 key matrix is significantly improved, with some use-cases where an unmodified key matrix would yield an avalanche effect of 0% would jump to 50% using the LFSR-enhanced key matrix.