Take for example I have my social security and other personal information stored as a string that I am trying to encrypt on my local drive. My first method of encrypting the string is to use a password based AES algorithm, and would then simply paste the generated cipher text into a file where I can store it and decipher it later. My second method of encrypting the string is to make up my own algorithm which is much more simple -- I take that string and apply a few easy bit shifts mixed with some random bit additions, multiplications, and rotations. Later if I need to decrypt that string, I can apply the negation of my logic to attain my decrypted string.
Now that we have a string encrypted with the popular AES algorithm, and another string encrypted with my silly algorithm, they both look equally jumbled up and complex.
Now let's assume that someone wanted to decrypt my personal information, having access to the simple text file that I stored their cipher text in. The attacker does not know what kind of an algorithm I used on the ciphered text. Which cipher text is going to be harder to decrypt? Does the algorithm that I used for this scenario actually matter and why? If this was a poor example of where encryption algorithm strength may matter, could you explain a better scenario of where it would matter more?
I'm failing to see how a complex algorithm holds up better than a weaker OR self-made closed source one, since I'm assuming that an attacker will attempt to use brute force. Since I'm assuming they would attempt brute force then I'm also assuming they have no control over how random their guesses are, (possibly)rendering algorithm strength to be useless -- i.e. since both strings are jumbled up and look random, they both appear complex.