Kostas Manes

Data Hiding Techniques in Steganography Using Fibonacci and Catalan Numbers

During the last decades, Steganography has found many applications. Many steganographic systems have been developed and used in various areas, e.g., in digital assets (DRM), Telecommunications, Medicine etc. In this paper, we prove that the set CF, which is a union of a certain set of Fibonacci numbers and a certain set of Catalan numbers, satisfies conditions, similar to those of Zeckendorfs Theorem. Therefore, it can be used for the encoding of data. Using this result, we propose a method that improves the Fibonacci data hiding technique.

Equivalence classes of ballot paths modulo strings of length 2 and 3

Two paths are equivalent modulo a given string

Social Networks Medical Image Steganography Using Sub-Fibonacci Sequences

\tau

Nonleft peaks in Dyck paths

, whenever they have the same length and the positions of the occurrences of

Data Hiding Techniques in Steganography Using Sub-Fibonacci Sequences

\tau

The average number of times a stack exceeds a certain size

are the same in both paths. This equivalence relation was introduced for Dyck paths in \cite{BP}, where the number of equivalence classes was evaluated for any string of length 2. In this paper, we evaluate the number of equivalence classes in the set of ballot paths for any string of length 2 and 3, as well as in the set of Dyck paths for any string of length 3.

Strings of Length 3 in Grand-Dyck Paths and the Chung-Feller Property

Social network sites such as Google+, Facebook, Linkedin and Twitter have become a significant part of our modern lives. It is very true that social networks have changed our lives in many ways. One of them is private messaging, through this, people can share not only messages but pictures, videos and sounds with other users. The ability of picture sharing gives users the opportunity to use social networks to exchange secret information using steganographic methods. Nowadays, the transmission of medical images is a daily routine and it is necessary to find an efficient way using steganography to transmit them securely over the social networks. In this paper we examine social networks picture sharing possibilities and we propose a unique and safe steganographic method using sub-Fibonacci sequences.

Counting strings at height j in Dyck paths

A peak in a Dyck path is called nonleft, if the ascent preceding it is greater than or equal to the descent following it. In this paper, we present a combinatorial construction of the set of Dyck paths of fixed semilength and number of nonleft peaks. As a bonus, we obtain various results on the enumeration of several kinds of peaks.

Recursive Generation of k-ary Trees

Recently, several steganographic methods, based on bitplane analysis have been developed. These methods improve the classical LSB method, generally by increasing the number of bitplanes via sophisticated encodings. In this paper, we show that these methods can be unified with the use of sub-Fibonnaci sequences. The huge number (trillions of them) of these sequences gives us the advantage to use them as cryptographic keys.

General Results on the Enumeration of Strings in Dyck Paths

We obtain an explicit as well as an asymptotic formula for the average number of times a stack exceeds a fixed size j, after the execution of n push operations. The stack is assumed to have limitless capacity and all possible sequences of push and pop operations are considered to be equally likely.