Messages hidden in plain sight, in words, invisible characters, pixels, sound, printed dots, stacked transparencies, DNA and the bytes of files, and the analyses that find them.
Visual Cryptography
Naor and Shamir’s visual cryptography (EUROCRYPT ’94): a picture shared out as transparencies, any k of n of which, laid over one another, show it to the eye while fewer tell nothing — secret sharing read without computing. Their schemes for up to six shares, each tested against their definition; two pictures that hide a third; the dot patterns their paper encloses.
Terms
About this tool
History
Moni Naor and Adi Shamir published visual cryptography in the proceedings of EUROCRYPT ’94: a page of what looks like random noise and a transparency of the same kind which, laid together, show a text. The eye does the decoding, and like a one-time pad each page needs a transparency of its own. They extended it to k out of n secret sharing, and to two innocent pictures, a house and a dog, that together show a third. Its full version ends with two dot patterns to try.
How it works
Each pixel of the secret becomes a block of subpixels on every share. A scheme is two matrices of black and white subpixels, a row a share, one for a white pixel and one for a black; each pixel takes its colour’s matrix with the columns shuffled at random. Stacked transparencies show the “or” of their rows: with k of them a black pixel is blacker than any white one, while fewer rows of the two matrices hold the same columns. The schemes are the paper’s: Figure 1’s 2 × 2 forms, its 2 out of 6 and 3 out of n matrices, Figure 2 and Construction 2. Hidden in two pictures, a share’s white is two black subpixels of four and its black three, as Figure 4 sets out.
How it was checked
Every scheme offered is tested against the paper’s Definition 2.1 exactly, the contrast for every k shares and the same columns for every fewer; the paper’s counts hold, and Figure 2 proves to be Construction 2 with a ninth subpixel black. Figure 5’s two patterns were read from the page at 600 dots an inch: every block is a diagonal form, and laid together 2,348 of the 8,192 blocks come out black and spell IACR. Moved a subpixel, the word shows reversed; a whole pixel, it is gone. One share’s six forms are as common under white pixels as under black, within a point.
Limits
The paper’s general k out of n construction needs far more subpixels than a print holds, so only its small schemes are offered, up to six shares, and its continuous-tone half circles are left out. Pictures become black and white at half grey, shares at most 400 × 300 subpixels; the two hiding pictures are words. Shares must be printed at one scale and laid exactly. The secret is never saved or put in a link.