I have a program that generates output data depending on the inputs it is given. Lets say the data generated is a list of n items where each item is a natural number between 1 and k. I need to release this data in such a way that an observer can't discern any patterns (e.g. if the ith item is 10, that is always followed by 15, 25, etc) or counts (the number of times a given number appears in the output list). So I want to add noise to this output list to achieve this property. How do I go about doing this?
I've looked a bit into Differential Privacy but I don't think this is applicable since there is no notion of "plausible deniability" with regards to my problem. Also, it is quite hard for me to determine the "sensitivity" of the output list to changes in the input because the underlying application is very complex. One point to note is that multiple runs of the application will produce random lists but the underlying patterns between the data items will be maintained and this is what I'd like to hide with noise.