Valery I. Korzhik

Key Distribution Protocols Based on Noisy Channels in Presence of an Active Adversary: Conventional and New Versions With Parameter Optimization

In this paper, we consider the information-theoretic secure key distribution problem over noisy wiretap channels with public discussion and in the presence of an active adversary. There are several well-known versions of the protocols proposed by Maurer and Wolf to solve this problem. We describe several new versions of the key distribution protocols for the same channel model allowing to increase the key rate given a fixed key security and under an optimization of the protocol parameters. Both asymptotic and nonasymptotic cases are presented. It is shown that in some cases the nonasymptotic key rate is not so far from the asymptotic one whenever the lengths of the transmitted strings are of the order of thousands of bits.

On the existence of perfect stegosystems

There are several steganography techniques (e.g. linguistic or least significant bit embedding) that provide security but no robustness against an active adversary. On the other hand it is rather well known that the spread-spectrum based technique is robust against an active adversary but it seems to be insecure against a statistical detection of stegosignal. We prove in this paper that actually this is not the case and that there exists an stegosystem that is asymptotically both secure to statistical detection and robust against a jamming of stegosignal by an active adversary. We call such stegosystems quasiperfect whereas we call them perfect if in addition the data rate of secret information is asymptotically constant. We prove that perfect stegosystems do not exist for both blind and informed decoders. Some examples using the simplex and the Reed-Muller codes jointly with stegosystems are given.

Watermarking of binary messages in conditions of an additive binary noise attack

We consider a private watermarking system (WM) for binary cover messages (CMs). The goal of an attacker is to render unable the WM-owner of WM detection without noticeable corruption of CMs. Here, we restrict the attackers activity to modulo two addition of a binary noise sequence to the watermarked stegomessage (SM). The formulas for the probabilities of WM-missing and WM-false alarm are obtained. We prove that the WM procedure can be designed to be reliable without significant distortions and for medium length of CMs even in the case in which CMs are unknown by the WM detector.

Secret Key Agreement Over Multipath Channels Exploiting a Variable-Directional Antenna

We develop an approach of key distribution protocol(KDP) proposed recently by T.Aono et al., where the security of KDP is only partly estimated in terms of eavesdroppers key bit errors. Instead we calculate the Shannons information leaking to a wire tapper and also we apply the privacy amplification procedure from the side of the legal users. A more general mathematical model based on the use of Variable-Directional Antenna (VDA) under the condition of multipath wave propagation is proposed. The new method can effectively be used even in noiseless interception channels providing thus a widened area with respect to practical applications. Statistical characteristics of the VDA are investigated by simulation, allowing to specify the model parameters. We prove that the proposed KDP provides both security and reliability of the shared keys even for very short distances between legal users and eavesdroppers. Antenna diversity is proposed as a mean to enhance the KDP security. In order to provide a better performance evaluation of the KDP, it is investigated the use of error correcting codes.

On the use of Bhattacharyya distance as a measure of the detectability of steganographic systems

It is very common to use the notion of relative entropy (or Kullback-Leibler divergence) as a measure for the discrimination difficulty among the hypotheses testing of presence and absence within a stegano-graphic system. Relative entropy is not a symmetric function and sometimes it is very hard to compute its values. We propose to customize the notion of Bhattacharyya distance to the solution of the same problem. The main properties of Bhattacharyya distance are presented. We show applications of this new steganographic system security criterion within the model with a Gaussian colored covertext and within spread-spectrum watermarking by a white Gaussian sequence.

Steganographic applications of the nearest-neighbor approach to Kullback-Leibler divergence estimation

We propose to use a method for divergence estimation between multi-dimensional distributions based on nearest neighbor distance (NND) for optimization of stegosystems (SG) and steganalysis. This approach has previously been effectively applied for the purposes of estimation and classification (particularly in the field of genetics). However, since divergence (precisely speaking, Kullback-Leibler divergence) is very popular in steganography, the NND approach can be used in order to estimate the security (undetectability) of stegosystems, given the known cover object corresponding to the tested SG. We will show how affects on the estimated divergence methods of image embedding and their parameters. This allows optimization of SG in relation to its security for the given cover images. Stegosystem detection based on the NND approach is also considered.

Image Authentication Based on Modular Embedding

We consider a watermark application to assist in the integrity maintenance and verification of the associated images. There is a great benefit in using WM in the context of authentication since it does not require any additional storage space for supplementary metadata, in contrast with cryptographic signatures, for instance. However there is a fundamental problem in the case of exact authentication: How to embed a signature into a cover message in such a way that it would be possible to restore the watermarked cover image into its original state without any error? There are different approaches to solve this problem. We use the watermarking method consisting of modulo addition of a mark and investigate it in detail. Our contribution lies in investigating different modified techniques of both watermark embedding and detection in order to provide the best reliability of watermark authentication. The simulation results for different types of embedders and detectors in combination with the pictures of watermarked images are given.

Achieveability of the Key-Capacity in a Scenario of Key Sharing by Public Discussion and in the Presence of Passive Eavesdropper

We consider a scenario of key sharing between a pair of legal users in the presence of passive eavesdropper. In this setting it is assumed the existence of a noisy channel between legal parties and also the existence of a noisy wire-tap channel (which is not necessary inferior to the main channel). In addition to noisy channel there is a noiseless public channel connecting legal parties. This means that eavesdropper can receive without errors all messages transmitted through this noiseless channel. Because eavesdropper is passive (by our assumption) this illegal party is unable to change any message transmitting by legal parties both over noisy and noiseless channel. The final goal of legal parties is to arrange such date exchange protocol using both noisy and noiseless channels that provides them with bit strings K A and K B of the same length l possessing the following properties: the probability P e of their discrepancy is close to zero; the amount of information I 0 about these strings leaking to eavesdropper is close to zero. Legal parties have nothing secret date shared in advance except the knowledge of protocol and channel parameters that are known also for eavesdropper. The key-rate R k is the ratio of the string length l to the length of the string transmitted between legal users through noisy channel. Key-capacity C k is the maximum possible key-rate when P e and I 0 approach both to zero. For some particular cases of noisy channels key-capacity has been found by U. Maurer. But it was open problem how to reach this capacity with limited computing power. The authors presented at previous MMM-ACNS’2001 workshop the constructive methods of key sharing for the same model. But for some channel parameters the key rates differed key-capacity in the several orders! In the current paper we use another protocol of key sharing and demonstrate how near to key-capacity can be provided the key-rate depending on complexity of key-sharing protocol.

Nonasymptotic estimates of information protection efficiency for the wire-tap channel concept

In this paper we have been considered the construction of code noising for the general case of the noising main channel and for codes with finite block length. It can be proved that such a construction is equivalent to the combined use of ordinary error correction codes and codes noising for a noiseless main channel. Therefore the complexity of code noising in the general case is at most that for ordinary error correcting codes.

Selective image authentication tolerant to JPEG compression

A watermark application in the integrity maintenance and verification of associated images is considered. There is a great advantage of watermark use in the context of conventional authentication since it does not require additional storage space for supplementary metadata. However JPEG compression, being a conventional method to compress images, leads to breaking of exact authentication. The usage of occuring selective authentication, tolerant to JPEG compression, is proposed. This technique is based on execution of Zernike moments. The performance evaluation of the proposed method depending on a compression factor is estimated. Simulation results show a good efficiency of this approach, including resistance to malicious attacks rather important within the frame of Security and Privacy in Future Generation Services topics.