Visual Cryptography

Visual Cryptography

| Moni Naor*and Adi Shamir
This paper introduces a new cryptographic scheme that allows for the decoding of concealed images without any cryptographic computations. The scheme is perfectly secure and easy to implement. It extends to a visual variant of the $k$ out of $n$ secret sharing problem, where a dealer provides transparencies to $n$ users, and any $k$ of them can see the image by stacking their transparencies, while fewer than $k$ users gain no information. The basic model involves a printed page of ciphertext and a printed transparency (secret key). The original message is revealed by placing the transparency over the ciphertext, as each transparency is indistinguishable from random noise. This system is similar to a one-time pad, with each page of ciphertext decrypted using a different transparency. The paper provides practical implementations of a $k$ out of $n$ visual secret sharing scheme for small values of $k$ and $n$, and asymptotic constructions that are optimal within certain classes of schemes. It also discusses efficient solutions for specific values of $k$ and $n$, such as 2 out of $n$ and 3 out of $n$ schemes. The authors propose two general constructions for any $k$ out of $k$ visual secret sharing problem, one using $2^k$ subpixels and another using $2^{k-1}$ subpixels. They prove that the second construction is optimal, showing that any $k$ out of $k$ scheme must use at least $2^{k-1}$ pixels. Additionally, they provide an upper bound on the relative difference $\alpha$ between the Hamming weights of combined shares from white and black pixels, proving that $\alpha \geq 2^{k-1}$. The paper also explores extensions of the basic model, including visual encryption of continuous-tone images and concealing the existence of the secret message. These extensions demonstrate the versatility and potential of the visual cryptographic scheme.This paper introduces a new cryptographic scheme that allows for the decoding of concealed images without any cryptographic computations. The scheme is perfectly secure and easy to implement. It extends to a visual variant of the $k$ out of $n$ secret sharing problem, where a dealer provides transparencies to $n$ users, and any $k$ of them can see the image by stacking their transparencies, while fewer than $k$ users gain no information. The basic model involves a printed page of ciphertext and a printed transparency (secret key). The original message is revealed by placing the transparency over the ciphertext, as each transparency is indistinguishable from random noise. This system is similar to a one-time pad, with each page of ciphertext decrypted using a different transparency. The paper provides practical implementations of a $k$ out of $n$ visual secret sharing scheme for small values of $k$ and $n$, and asymptotic constructions that are optimal within certain classes of schemes. It also discusses efficient solutions for specific values of $k$ and $n$, such as 2 out of $n$ and 3 out of $n$ schemes. The authors propose two general constructions for any $k$ out of $k$ visual secret sharing problem, one using $2^k$ subpixels and another using $2^{k-1}$ subpixels. They prove that the second construction is optimal, showing that any $k$ out of $k$ scheme must use at least $2^{k-1}$ pixels. Additionally, they provide an upper bound on the relative difference $\alpha$ between the Hamming weights of combined shares from white and black pixels, proving that $\alpha \geq 2^{k-1}$. The paper also explores extensions of the basic model, including visual encryption of continuous-tone images and concealing the existence of the secret message. These extensions demonstrate the versatility and potential of the visual cryptographic scheme.
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