Image steganography hides multiple images for multiple recipients into a single cover image. All secret images are usually revealed without authentication, which reduces security among multiple recipients. It is elegant to design an authentication mechanism for isolated reception. We explore such mechanism through sufficient experiments, and uncover that additional authentication information will affect the distribution of hidden information and occupy more hiding space of the cover image. This severely decreases effectiveness and efficiency in large-capacity hiding. To overcome such a challenge, we first prove the authentication feasibility within image steganography. Then, this paper proposes an image steganography network collaborating with separate authentication and efficient scheme. Specifically, multiple pairs of lock-key are generated during hiding and revealing. Unlike traditional methods, our method has two stages to make appropriate distribution adaptation between locks and secret images, simultaneously extracting more reasonable primary information from secret images, which can release hiding space of the cover image to some extent. Furthermore, due to separate authentication, fused information can be hidden in parallel with a single network rather than traditional serial hiding with multiple networks, which can largely decrease the model size. Extensive experiments demonstrate that the proposed method achieves more secure, effective, and efficient image steganography. Code is available at https://github.com/Revive624/Authentication-Image-Steganography.

In Eurocrypt'18, Cid et al. proposed a new cryptanalysis tool called Boomerang Connectivity Table (BCT), to evaluate S-boxes of block ciphers. Later, Boura and Canteaut further investigated the new parameter Boomerang uniformity for cryptographic S-boxes. It is of great interest to find new S-boxes with low Boomerang uniformity for even dimensions. In this paper, we prove that a class of permutation quadrinomials over F2(2m)with m odd has Boomerang uniformity four, which gives the fifth class of such kind of permutation polynomials. Further, the occurrences of 0 and 4 in the BCTs of the investigated permutation polynomials are also completely determined.