The keys it is sending appear to be in pairs, in sets of 16, if you concatenate them you get the 32bit entire key. All of the keys are presented in hexadecmial format, you will notice none of the letters go above f. Most of the keys sent end in eight 0's, this would me to believe that this is padding and infact, the two keys concatenate to build up one 32bit string, but if you look carefully you will note that some of them only have 7bits of padding on the end, so I will disregard this assumption.

These tweets appear to originate from Russia.

Now, common uses of 16bit (and 32bit) encryption keys are for WEP keys, traditionally used in router password protection, which can be provided either in a full ASCII spectrum or in merely hexadecimal format.

Taking these points together I can conclude that these could possibly be the encrypted WEP keys of a Russian router.

Or I could be totally wrong, but I really wasn't given much to work with :)