No, jQuery, don't processData!

processData (default: true)
Type: Boolean
By default, data passed in to the data option as an object (technically,
anything other than a string) will be processed and transformed into a
query string, fitting to the default content-type
"application/x-www-form-urlencoded". If you want to send a DOMDocument,
or other non-processed data, set this option to false.

https://api.jquery.com/jQuery.ajax/

js/api.js

@@ -266,6 +266,7 @@ window.textsecure.api = function() {
                     type        : "PUT",
                     headers     : {"Content-Type" : "application/octet-stream"},
                     data        : encryptedBin,
+                    processData : false,
                     success     : function() {
                         try {
                             // Parse the id as a string from the location url