# Xor

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 May15 comment Can A PRNG Be Used To Generate Multiple Private Keys for ECDSA?@DavidSchwartz: First, let me say that I really appreciate your responses, as well as CodeInChaos's answer. I agree with your conclusions, and am mostly being pedantic for the sake of clarity and education. I have further things I would like to quibble on ... but the comment length restriction on StackExchange makes these discussions difficult, so I think I will have to cut the discussion short. Thank you again for your time and help. May14 comment Can A PRNG Be Used To Generate Multiple Private Keys for ECDSA?According to WikiPedia, the only requirements for a CSPRNG are passing the "next-bit test" and withstanding "state compromise extensions". Qa does not give you information about a. So, being able to calculate Qb from Qa does not allow you to predict b from a. Thus, it does not violate either of the two requirements for a CSPRNG. Example: Suppose PRF(0) = 0, PRF(i) = PRF(i-1) + 1. It can be shown that Qb = Qa + G, and that b = a + 1. But neither b nor a can be calculated. May14 awarded Scholar May14 accepted Can A PRNG Be Used To Generate Multiple Private Keys for ECDSA? May13 comment Can A PRNG Be Used To Generate Multiple Private Keys for ECDSA?That was my intuition as well, and thank you for the response. Here is my issue: If a and b are sequential outputs from a CSPRNG, calculating b from a should be intractable or impossible. This is as you said, and is indeed the requirement for a CSPRNG. However, I cannot figure out a way to logically prove that calculating public key Qb from Qa must also be intractable, given the above, and given that Qb = b*G and Qa = a*G. I agree with your intuition that it must be so ... but I just can't figure out a logical proof for it. May13 awarded Student May13 asked Can A PRNG Be Used To Generate Multiple Private Keys for ECDSA?