Is this property implied by a pseudorandom function?

Link L

6/14/23, 3:51 AM

Given a keyed pseudorandom function $f: S \times X \rightarrow Y$, where $S$ is the space of secret keys, $X$ is the input domain, and $Y$ is the range, the pseudorandom property says that given any secret key in $S$ the uniform distribution over $Y$ is indistinguishable from the distribution of $f(X)$.

Am wondering, does this property imply also the following:

Let $f: S \times X \rightarrow Y$ be a pseudorandom function. GIven $x \in X$ and $y \in Y$, it is computationally difficult to determine the secret $s \in S$ such that $f(s,x) = y$.

If true, does anyone know a name for this property ?

0 + 0

pseudo-random-function

pseudo-random-generator

knaccc

6/14/23, 4:09 AM

"security against key recovery", or more simply "secure".

Link L

6/14/23, 4:10 AM

@knaccc thank you ! ... is security against key recovery implied by pseudorandomness ? thanks

Mikero

6/14/23, 4:19 AM

Is this homework? Think about the contrapositive of "if its outputs are indistinguishable from random then it is secure against key recovery attacks"

Link L

6/14/23, 4:27 AM

@Mikero, thanks ... not homework but I saw an article from doctor google which says that PRF is actually a stronger property than key recovery

fgrieu

6/14/23, 9:42 AM

I have a problem with the use of "given" in "given any secret key". To me, a given is available. I'd use "for" instead.

kelalaka

6/14/23, 10:40 AM

If you can recover the key, then it is not PRF anymore.

Elon Musk

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

EN: Is this property implied by a pseudorandom function?

TH: คุณสมบัตินี้บอกเป็นนัยโดยฟังก์ชันหลอกเทียมหรือไม่

RO: Această proprietate este implicată de o funcție pseudoaleatoare?

RU: Подразумевается ли это свойство псевдослучайной функцией?

VI: Thuộc tính này có được ngụ ý bởi hàm giả ngẫu nhiên không?

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