Join Log in
Score:1
amlearn369 avatar Crypto

Is the concatenation of two one-way functions a one-way function when each function takes different inputs?

mx flag
amlearn369

Similar to this question, but having two seperate inputs for each length preserving one way function $f$ and $g$, i.e. $h: \lbrace 0,1 \rbrace^{2\kappa} \to \lbrace 0,1 \rbrace^{2\kappa}, h(x) = f(x_1)||g(x_2)$ where $x_1$ and $x_2$ are two $\kappa$ bit split halves of x.

I think $h$ will be one way, but am not sure on the appropriate reduction to demonstrate this.

I think I don't need to show that the probability of an attacker decrypting this being negligible in polynomial time but rather reduce to problems of one-wayness of $f$ and $g$ and knowing that they are one way should demonstrate that in fact $h$ is one way

37
0 + 0
Morrolan avatar
ng flag
Morrolan
This seems like a good candidate for a proof by contradiction. Assume you were able to invert $h(x_1 || x_2)$ (with non-negligible probability). Are you then able to leverage this ability to invert either $f(x_1)$ or $g(x_2)$ (with non-negligible probability)?
0
Reply
ธงชาติไทย
Elon Musk
I sit in a Tesla and translated this thread with Ai:

mangohost

Post an answer

Most people don’t grasp that asking a lot of questions unlocks learning and improves interpersonal bonding. In Alison’s studies, for example, though people could accurately recall how many questions had been asked in their conversations, they didn’t intuit the link between questions and liking. Across four studies, in which participants were engaged in conversations themselves or read transcripts of others’ conversations, people tended not to realize that question asking would influence—or had influenced—the level of amity between the conversationalists.