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Is there any special parameters for using SHA-1 for generating pseudo-random numbers? What are the differences between SHA-1 as a PRNG and original SHA-1?

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There are many possible constructions but the simplest is probably to initalize a counter with a random seed and hash the counter to produce more random bits and then increment the counter.

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  • $\begingroup$ And what about having a sequence made by using SHA-1 on the previous hash and having some big number as a starting value? (it will be a seed). counter=10 seed=12345 r=sha1(seed) for i in range(counter): ` print(r)` #making new random number ` r=sha1(r)` Will it be ok? $\endgroup$ – R Georgy Nov 2 '19 at 18:04
  • $\begingroup$ Yes, that is also ok, you are expected to repeat after aproximately 2^80 steps which is less than what I proposed but should still be sufficient for most purposes. SHA-1 is not considered secure but due to no viable pre-image attack I do not know of a viable attack on either construction. Regardless of PRNG you need a high entropy seed for security. $\endgroup$ – Meir Maor Nov 2 '19 at 18:19
  • $\begingroup$ What? No! That is not OK! The function $k \mapsto H(k) \mathbin\| H(H(k)) \mathbin\| H(H(H(k))) \mathbin\| \dotsb$ is absolutely not a secure pseudorandom generator. Anyone who sees one block of output can trivially predict all subsequent blocks of output. $\endgroup$ – Squeamish Ossifrage Nov 3 '19 at 14:52
  • $\begingroup$ Yes of course, it only works if you output a small part of your state. $\endgroup$ – Meir Maor Nov 3 '19 at 17:55

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