I have a base64 'cipher' text. I know that in clear text is a hidden XML document (I know nothing about its structure), but the base64 alphabet was somehow shuffled. Is there any smart way, how to detect the modified alphabet better than checking all 64! permutations? I can slightly reduce the number of permutations by using the knowledge that XML document starts (without doctype, just root element) with opening tag (character '<') and ends with '>'. But there are still 62! permutations which are still not computable.
I have also tried to infer some other characters, but as the tags may be arbitrarily long and the content may be any character, I don't see much space for frequency analysis.