Constructing Perfect Steganographic Systems

We propose steganographic systems for the case when covertexts (containers) are generated by a finite-memory source with possibly unknown statistics. The probability distributions of covertexts with and without hidden information are the same; this means that the proposed stegosystems are perfectly secure, i.e. an observer cannot determine whether hidden information is being transmitted. The speed of transmission of hidden information can be made arbitrary close to the theoretical limit - the Shannon entropy of the source of covertexts. An interesting feature of the suggested stegosystems is that they do not require any (secret or public) key. At the same time, we outline some principled computational limitations on steganography. We show that there are such sources of covertexts, that any stegosystem that has linear (in the length of the covertext) speed of transmission of hidden text must have an exponential Kolmogorov complexity. This shows, in particular, that some assumptions on the sources of covertext are necessary

FULLY HOMOMORPHIC ENCRYPTION FOR WIRELESS NETWORK

This work provides a mathematical approach of the Fully homomorphic encryption (FHE) and its implementation in a wireless network. FHE has been presented as the Holy Grail by the cryptographers. This special encryption scheme enables one to perform complex operations(both addition and multiplication) on a cypher text without ever decrypting the text. An immediate application is the delegated computation, an untrusted party can process the data without endangering the privacy of the source and the integrity of the data. The first FHE scheme was introduced in 2009, by Craig Gentry. His scheme was based on the properties of rings especially on ideal lattices.As introduced by Gentry, FHE was not practical due to the length of ciphertext (per bit encrypted) and the keys, and its infeasible computational time. Many works have been done to make it somewhat practical(Shai-Halevi(2010), Smart-Vercauteren(2011)).The proposed schemes were based on algebra and number theory concepts. Following the idea of Smart-Vercauteren, and the implementation of Michael Brenner we design an implementation for wireless network. Such a system should allow operations on encrypted data that could result in reducing the computation load and the size of the packets in a wireless network. The most challenging part of this work will be to make the computational time of the FHE quasi real while preserving its security scheme. Since the strength of the FHE comes from the hardness to approximate short vector problems on arbitrary lattices within a slightly super polynomial factor, making that computational time logarithmic or less is quite challenging. This work attempts to design and implement fully homomorphic encryption for wireless networks

Performance Comparison of Projective Elliptic-curve Point Multiplication in 64-bit x86 Runtime Environment

For over two decades, mathematicians and cryptologists have evaluated and presented the theoretical performance of Elliptic-curve scalar point-multiplication in projective geometry. Because computation in projective domain is composed of a wide array of formulations and computing optimizations, there is not a comprehensive performance comparison of point-multiplication using projective transformation available to verify its realistic efficiency in 64-bit x86 computing platforms. Today, research on explicit mathematical formulations in projective domain continues to excel by seeking higher computational efficiency and ease of realization. An explicit performance evaluation will help implementers choose better implementation methods and improve Elliptic-curve scalar point-multiplication. This paper was founded on the practical solution that obtaining realistic performance figures should be based on more precise computational cost metrics and specific computing platforms. As part of that solution, an empirical performance benchmark comparison between two approaches implementing projective Elliptic-curve scalar point-multiplication will be presented to provide the selection of, and subsequently ways to improve scalar point-multiplication technology executing in a 64-bit x86 runtime environment