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Lets say I have a string of n bits that needs to be filled by repeatedly applying some function on k strings of m bits where |m|<|n|. Assuming that m(i) is a random string and n needs to also be random what is the best way to do this. Note it is possible that k*|m|>|n|. What I have been thinking so far is:

~    Let m' be the average length of m       // this is pre-computable
~    Let n be all 0's

~    for i=0 --> k
~       pos=m'*i

~       xor string k[i] onto n starting at pos   // wrap around if needed

~ While this is simple I wonder if it can be attacked (determine what k[i]) if k*|m|>|n| (it is trivial to attack if k*|m|<=|n|). Also is there some way to make attacking hard if k*|m|<=|n|?

~    Ideas?
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