Cracking Strings from URLs

I've got long strings like this from URLs (percent-encoded
characters have been decoded):

SdADygkIiM8ED8ZK/ZfkxwbHEgOXnsgKzQcYtq2j3L1HN6OYvET8PwvO2gpCCv4Bp4vIGLwLFN3dDQABOjWT0gVI/EtBlNUIObwLFNnU90IK/gCs2QQzBzhEz8sNAAdBPpmM+T0KRgudx88HxzsFnpjGQs8PBp+fEAvQCgCZnsdKzQz+lpbIBPj7CQ==

I believe they might be encrypted strings containing one or more
known fields, probably including a known ten digit number
(1409518286 in that case). They might also be hashes, but I think
it's unlikely.

Are there any simple Linux tools that can help identify and crack
the algorithm by checking combinations of the known strings that
it's likely to contain? Similar to what John The Ripper
does for password hashes by checking against dictionaries of
common passwords. Then I could write code to decrypt the other
strings.

I think the PHP scripts generating the strings were first written
well over twenty years ago, so I'm guessing it's nothing all that
sophisticated.

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