Is concatenation of two distinct secure PRG still secure?

M0S1AM

10/27/23, 5:10 PM

I'm new to cryptography and having a hard time understanding PRGs and PRFs.

Question: $G'(x)$ and $G''(x)$ are two different secure pseudorandom generators, and $G(x)=G'(x) \mathbin\Vert G''(x)$.

Is $G(x)$ still a secure

I thought $G(x)$ is secure at first, since $G'(x)$ and $G''(x)$ are secure, their outputs are uniform.

But I think it's not supposed to be correct later, since concatenation of them does not mean it's uniform.

138

0 + 3

pseudo-random-generator

Maarten Bodewes

10/27/23, 11:06 PM

"since concatenation of them does not mean it's uniform" why do you think that is the case? Note that your 3rd sentence has not been completed. I would expect "PRG?", but given your first sentence it could be PRF too (although that doesn't make much sense semantically if you ask me).

yyyyyyy

10/28/23, 3:23 AM

**Hint:** "different" does not necessarily imply "unrelated".

Gordon Davisson

10/28/23, 3:57 AM

Related question: ["Concatenation of two strong hashes may have striking weakness"](https://crypto.stackexchange.com/questions/24488/concatenation-of-two-strong-hashes-may-have-striking-weakness).

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: Is concatenation of two distinct secure PRG still secure?

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