How to compute $x_0$ in Chaotic Logistic map in special method?

Mhsz

10/18/23, 10:14 PM

I know that the Chaotic Logistic map is $x_{n+1}=Rx_n(1−x_n)$. I read some articles about the Chaotic Logistic Map, but some things are not clear. Someone wrote in his article the following: The initial condition $x_0$ for the logistic map is extracted from the string of $256$ bits ($32$ characters) taken in ASCII form and denoted as $K=K_1,K_2,K_3,\cdots,K_{32}$ ($K_i$ denotes the $8$-bit key character in the $i$-th key position). The value of the initial condition for the logistic map is given by.

\begin{equation} x_0=\sum_{i=1}^{32}\text{mod}(K_i\times 10^i,1) \end{equation} Another author wrote the following

My question: How does he calculate $x_0$ in that function, where we know $x_0$ should lie within the interval $[1,0]$.

0 + 4

cryptanalysis

Daniel S

10/19/23, 5:43 AM

Are you sure that the summands are not $\mathrm{mod}(K_i\times 10^{-i},1)$?

Mhsz

10/19/23, 7:15 PM

Yes I am sure..

Mhsz

10/19/23, 7:24 PM

See for modifying my question.

fgrieu

10/20/23, 7:23 AM

The literature on cryptographic applications of the Chaotic Logistic map is riddled with errors (and the whole subject is seldom treated seriously or published in reputable journals on cryptography). The equation that the question considers uses non-standard notation, and seems stuck to $x_0=0$. If for some reason it's really needed to work on something similar, what about using$$x_0=\frac{\left(\displaystyle\sum_{i=1}^{32}K_i\times 10^{i-1}\right)\bmod10^{32}}{10^{32}}$$which at least uses standard notation and can take $10^{32}$ values all in $[0,1)$?

Elon Musk

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

EN: How to compute $x_0$ in Chaotic Logistic map in special method?

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.