Bounds for Visual Cryptography Schemes

In this paper, we investigate the best pixel expansion of the various models of visual cryptography schemes. In this regard, we consider visual cryptography schemes introduced by Tzeng and Hu [13]. In such a model, only minimal qualified sets can recover the secret image and that the recovered secret image can be darker or lighter than the background. Blundo et al. [4] introduced a lower bound for the best pixel expansion of this scheme in terms of minimal qualified sets. We present another lower bound for the best pixel expansion of the scheme. As a corollary, we introduce a lower bound, based on an induced matching of hypergraph of qualified sets, for the best pixel expansion of the aforementioned model and the traditional model of visual cryptography realized by basis matrices. Finally, we study access structures based on graphs and we present an upper bound for the smallest pixel expansion in terms of strong chromatic index

Using graphic methods to challenge cryptographic performance

Block and stream ciphers have formed the traditional basis for the standardisation of commercial ciphers in the DES, AES, RC4, and so on. More recently alternative graphic methods such as Elliptic Curve Cryptography (ECC) have been adopted for performance gains. In this research we reviewed a range of graphic and non-graphic methods and then designed our own cipher system based on several graphic methods, including Visual Cryptography (VC). We then tested our cipher against RC4 and the AES algorithms for performance and security. The results showed that a graphics based construct may deliver comparable or improved security and performance in many of the required areas. These findings offer potential alternative avenues for post-quantum cryptographic research