Question

Let G be a pseudorandom generator that maps n-bit inputs to (n+1)-bit outputs, and define G' (81, ..., Sn) = G(81, ..., Sn)||($1 1 s2). Here $1,..., Sn are the bits of the seed s, and || denotes concatenation. Is G' a pseudorandom generator?

Answer 1

The requirements for a pseudorandom generator is basically that you should generate random numbers, which has no relationship with its meaning or actually can be derived from the seed without generator i.e it should have a avalanche effect in its construction.

Here the result will have G which is pseudo random number generator and even if we add one extra bit at the end it wouldn't make any difference.

So yes, even if we add just one bit changes anything in it the total will change drastically so yes.

This also tells us that we can generate our own random generator from a existing one, or by mixing two .

Hope it helps