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I have been reading about shift register based keystream generators in cryptography. One usual method of generating keystream sequences is feeding the output of several Linear Feedback Shift Registers to a "memoryless nonlinear Boolean fuction". I googled around about memoryless functions but I haven't found much about Boolean ones.

Can somebody explain what a memoryless boolean function is?

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Actually this term was in the context of the particular textbook. In fact, in the next section a keystream generator is introduced, where the output of the Linear Feedback Shift Register is fed to a Boolean function but there is also a "memory function" that saves (part of) the previous LFSR state. This previous LFSR state is also fed to the Boolean function. Then this boolean function is called a "Boolean function with memory". When we have a keystream generation where a memory function does not exist, then we have a "memoryless" Boolean function.

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