Can a security parameter be used in a function that combines pseudorandom generators?

Nina

5/30/23, 4:52 PM

I am really stuck with the following question:

$G: \{0,1\}^\lambda \to \{0,1\}^{2\lambda}$ is a secure pseudorandom generator, and $\lambda$ is a security parameter.

Is the following a secure pseudorandom generator? $$G'(s_1,s_2) = (s_1 \oplus 1^\lambda, G(s_1))$$

What confuses me about this is the use of the security parameter in the $G'$ function. Can the security parameter be used in this way? If yes, how can I go by determining if $G'$ is secure?

0 + 0

pseudo-random-generator

Nina

5/30/23, 5:06 PM

Thank you! And if you XOR s1 with all 1's, it should not make H any less secure, right? Do you understand what it means here that s2 is not present in (1⊕1,(1))?

kelalaka

5/30/23, 5:12 PM

It means all 1's of size $\lambda$. Complement $s_1 \oplus 1^\lambda$ then check that second component is $G(s_1)$. It discards the input. It can still be expanding, though. I've changed $G$ and $G'$ as this more common notation ( $G$ from Generator). You can use $\LaTeX$/MathJax in the questions, answers, and comments, too. See my edits.

meshcollider

5/30/23, 10:51 PM

Remember that the security of a pseudo-random number generator considers whether you can tell the output apart from truely random. That should be sufficient info to complete the question :)

kelalaka

5/31/23, 12:30 AM

Nina, you can write your answer, we will be happy about this. This will increase your skill since we will argue and correct your answer.

Elon Musk

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

EN: Can a security parameter be used in a function that combines pseudorandom generators?

TH: สามารถใช้พารามิเตอร์ความปลอดภัยในฟังก์ชันที่รวมตัวกำเนิดเทียมเทียมได้หรือไม่

RO: Poate fi folosit un parametru de securitate într-o funcție care combină generatoare pseudoaleatoare?

RU: Можно ли использовать параметр безопасности в функции, объединяющей генераторы псевдослучайных чисел?

VI: Có thể sử dụng tham số bảo mật trong hàm kết hợp trình tạo giả ngẫu nhiên không?

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