Example of Pixel-based Visual Cryptography in Detail
All that is not perfect down to the smallest detail is doomed to perish.
Gustav Mahler 266 Example of Pixel-based Visual Cryptography
Figure 1: Example: Pixel-based Visual Cryptography, Original Picture
S. Pape, Authentication in Insecure Environments, DOI 10.1007/978-3-658-07116-5, © Springer Fachmedien Wiesbaden 2014 Example of Pixel-based Visual Cryptography 267
Figure 2: Example: Pixel-based Visual Cryptography, Transparency 1 268 Example of Pixel-based Visual Cryptography
Figure 3: Example: Pixel-based Visual Cryptography, Transparency 2 Example of Pixel-based Visual Cryptography 269
Figure 4: Example: Pixel-based Visual Cryptography, Overlay Auxiliary Tables and Proofs
Consistency is found in that work whose whole and detail are suitable to the occasion. It arises from circumstance, custom, and nature.
Marcus Vitruvius Pollio 272 Auxiliary Tables and Proofs
Lemmas ( )= − 2 n Lemma 11.1. The derivative of f n 1 n+1 is positive for all n>1.
v v Proof. By applying the chain rule for df f(n)=du du + du dv dn du dn dv dn v v with u = 1 − 2 , v = n, du = vuv−1, and du = log(u)uv it follows: n+1 du dv − df 2 n 1 df 2 f(n)=n 1 − 1 − dn n + 1 dn n + 1 2 n 2 df + 1 − log 1 − (n) n + 1 n + 1 dn − 2 n 1 2 2 2 = 1 − n + 1 − log 1 − n + 1 (n + 1)2 n + 1 n + 1 2 n 2n n − 1 = 1 − + log n + 1 n2 − 1 n + 1