1
$\begingroup$

I'm starting to study about visual cryptography, but I am stuck with the following problem.

On paper "Visual Cryptography" by Moni Naor and Adi Shamir, on page 6. How to read/what is the meaning of

$$J^0_i = 0^{i-1}10^{k-i}$$

and

$$J^0_k = 1^{k-1}0$$

where $1 \le i \le k$?

Can someone explain how to read it? Because I think I misunderstood.. And also I'm happy if anyone gives me a reference to learn it.

$\endgroup$
2
$\begingroup$

This is string notation: $J_i^0=0^{i-1}10^{k-i}$ means i-1 consecutive 0's followed by a 1 (we don't write $1^1$) which is then followed by k-i consecutive 0's. So $0^{3}10^{4}$ is $00010000$.

As for $S^t[i,x]=\langle J_i^t,x\rangle$, with $t\in \{0,1\}$ this is an inner product of $J_i^t$ with $x=(x_1,\ldots,x_k) \in \{0,1\}^k$ so in general $S^t[i,x]=x_i$ (only the 1 component in $J_i^0$ picks up a nontrivial value. Thus $S^0[2,x]=0\times x_1+1\times x_2+0\times x_3=x_2$ and $S^0[2,101]=0,$ while $S^0[2,010]=1.$ I agree it is quite cumbersome.

Generally, a good idea is to try to find "slides" as opposed to papers, where examples are usually given to make notations clear.

$\endgroup$
  • $\begingroup$ Hi kodlu, thanks for the answer and sorry for late reply.. I see.. but still confused, for example on that page, if k = 3, so J_1^0 = 100, J_2^0 = 010, J_3^0 = 001, right? then on next paragraph, S^t be defined as follows S^t[i,x] = <J_i^t, x> for any 1 <= i <= k and any vector x of length over GF[2]. So, it means that x is random vector? So, I dunno the meaning when t = 0, i = 1, x = 000, S^0[1,000] = <J_1^0, 000>, what is that? Sorry I am not good at it $\endgroup$ – stranger Oct 20 '15 at 4:51
  • $\begingroup$ sorry for late reply.. I just found the slide that you mention.. thankyou very much kodlu :) $\endgroup$ – stranger Nov 4 '15 at 17:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.