A $(k, n)$-Secret Image Sharing With Steganography Using Generalized Tent Map

Abstract

Secret Image Sharing (SIS) transfers an image to mutually suspicious receivers as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> meaningless shares, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> or more shares must be present to recover the secret. This paper proposes a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(k, n)$</tex>-SIS system for any image type using polynomial interpolation based on Lagrange polynomials, where the generated shares are of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1/k$</tex> of the secret image size. A full encryption system, consisting of substitution and permutation stages, is employed by using the generalized Tent map as a source of randomness. In addition to using a long and sensitive system key, steganography using the Least Significant Bits (LSBs) embedding technique is utilized to improve security. Detailed experimental analysis of the security, robustness and performance of the proposed system is provided, which is more comprehensive than the analyses given in other related works. Security is demonstrated using statistical tests, and robustness against noise and cron attacks is validated.