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Streaming Data String Transducers (SDSTs) were introduced to model a class of imperative and a class of functional programs, manipulating lists of data items. These can be used to write commonly used routines such as insert, delete and reverse. SDSTs can handle data values from a potentially infinite data domain. The model of Streaming String Transducers (SSTs) is the fragment of SDSTs where the infinite data domain is dropped and only finite alphabets are considered. SSTs have been much studied from a language theoretical point of view. We introduce data back into SSTs, just like data was introduced to finite state automata to get register automata. The result is Streaming String Register Transducers (SSRTs), which is a subclass of SDSTs. SDSTs can compare data values using a linear order on the data domain, which can not be done by SSRTs. We give a machine independent characterization of SSRTs with origin semantics, along the lines of Myhill-Nerode theorem. Machine independent characterizations for similar models have formed the basis of learning algorithms and enabled us to understand fragments of the models. Origin semantics of transducers track which positions of the output originate from which positions of the input. Although a restriction, using origin semantics is well justified and known to simplify many problems related to transducers. We use origin semantics as a technical building block, in addition to characterizations of deterministic register automata. However, we need to build more on top of these to overcome some challenges unique to SSRTs.