[OT] looking for a algorithm

[Aryeh M. Friedman]

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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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