I'm not an Imam but I feel like if someone wanted to justify using a Western created algorithm they could just say "well technically this is just built on our initial work"
I don't think that's true. Algebra has history that goes way back to Babylonian times, long before Islam.
From https://en.wikipedia.org/wiki/History_of_algebra
> The origins of algebra can be traced to the ancient Babylonians,[6] who developed a positional number system that greatly aided them in solving their rhetorical algebraic equations. The Babylonians were not interested in exact solutions, but rather approximations, and so they would commonly use linear interpolation to approximate intermediate values.[7] One of the most famous tablets is the Plimpton 322 tablet, created around 1900–1600 BC, which gives a table of Pythagorean triples and represents some of the most advanced mathematics prior to Greek mathematics.[8]
Islam is much more recent than that. From https://en.wikipedia.org/wiki/Islam#History
> Muhammad and the beginning of Islam (570–632)
From the History of Algebra Wikipedia link:
> "Al-Khwarizmi's text can be seen to be distinct not only from the Babylonian tablets, but also from Diophantus' Arithmetica. It no longer concerns a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study. On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."
Islam is, in fact, responsible for the first known treatise on cryptanalysis of simple substitution ciphers. One technique is assuming a letter begins "In the name of Allah" and working out letter values from there; another technique is counting letters, noting that alif and lam are the most frequent ones.