We propose a new key sharing protocol executed through any constant parameter noiseless public channel (as Internet itself) without any cryptographic assumptions and protocol restrictions on SNR in the eavesdropper channels.This protocol is based on extraction by legitimate users of eigenvalues from randomly generated matrices.A similar protocol was proposed recently by G. Qin and Z. Ding.But we prove that, in fact, this protocol is insecure and we modify it to be both reliable and secure using artificial noise and privacy amplification procedure.Results of simulation prove these statements.

The method of secret key sharing between units that did not possess any secret keys in advance is considered.It is assumed that between these units there are duplex wireless MIMO fading channels.In a recent paper published by D. Qin and Z. Dingh a new key sharing protocol has been proposed between legitimate users based on eigenvalues which are invariant under permutation of two matrices in their product.We extend this statement to a characteristic polynomial and by the way to matrix trace.Methods of key bits extraction are optimized both theoretically and experimentally.On the contrary to a statement of D. Qin and Z. Ding we prove that their key sharing protocol occurs insecure if eavesdroppers have the same channels as legitimate users.In order to provide reliability and security of the shared keys both error correction codes and privacy amplification methods can be used.

We consider a digital watermarking system intended for an embedding of additional information into audio (typically musical) files that should be resistant against a removal attack.The proposed embedding procedure is based on a reverberation and extraction procedure executing a cepstral transform.A removal attack based on blind dereverberation is investigated both theoretically and experimentally.In order to prevent such an attack, a slight modification of the embedding procedure is also proposed.Further experiments show that the proposed watermarking system provides both a good quality of the cover audio-signal and a sufficiently large embedding rate.

The method of key sharing between a mobile unit and a base station through a wireless MIMO-based fading channel is investigated.The description of a key distribution protocol is given.The expression to estimate the correct key bit agreement based on the use of guard interval is proved.Statistical properties of the key string are tested using the NIST criteria.Impossibility of key string eavesdropping by illegal users is guaranteed due to small values of correlation between legal and eavesdropper carrier phases.Numerical examples show that the MIMO system with 8 antennas is able to agree 256 bits with a reliability value 0.99 for SNR equal to 35 dB.This experiment confirms that the MIMO scenario is especially effective for secret key distribution.

The HUGO project, published at 2010, can be considered as one of the most promising direction in the design of highly undetectable steganography. The main idea of that approach is to minimise the embedding impact from the steganalysis point of view. This goal is achieved by using trellis codes in the embedding procedure, the Viterbi algorithm (VA) and the SPAM features. But the optimality of VA was kept still unclear because a generic purpose of VA is to correct errors with trellis codes instead of embedding secret information. The first goal of the current paper is to prove the optimality of VA application in its generalised form proposed about 30 years ago by one of the authors of this paper. The second goal is to optimise the parameters of the trellis code check matrix for better undetectability of stegosystems.

In this contribution we introduce a low-complexity bit-parallel algorithm for computing square roots over binary extension fields. Our proposed method can be applied for any type of irreducible polynomials. We derive explicit formulae for the space and time complexities associated to the square root operator when working with binary extension fields generated using irreducible trinomials. We show that for those finite fields, it is possible to compute the square root of an arbitrary field element with equal or better hardware efficiency than the one associated to the field squaring operation. Furthermore, a practical application of the square root operator in the domain of field exponentiation computation is presented. It is shown that by using as building blocks squarers, multipliers and square root blocks, a parallel version of the classical square-and-multiply exponentiation algorithm can be obtained. A hardware implementation of that parallel version may provide a speedup of up to 50% percent when compared with the traditional version.

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.

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 attacker's 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.

Before stating the results we would like to thank the referee for reorganizing the whole paper and changing its original logical terminology to an algebraical terminology. Let Z* be a proper elementary extension of the integral domain Z. For any b ∈ Z*∖Z we define Z〈b〉 as the following subring of Z*: It is easy to prove that the natural divisibility relation on Z〈b〉 is the restriction to Z〈b〉 of the divisibility on Z* (see Lemma 1.1 below). The much stronger statement that Z〈b〉 is algebraically closed in Z* does not hold for all b. Similarly, there are many b's such that Z〈b〉 is not a recursive ring, e.g. if the set of standard primes dividing b is not recursive then Z〈b〉 cannot be a recursive ring under any bijection with N. Our main result is the following. Theorem. There exists an element b ∈ Z*∖Z such that (1) Z〈b〉 is algebraically closed in Z*, (2) Z〈b〉 is a recursive ring, and (3) each infinite element of Z〈b〉 is divisible by a standard integer > 1 (so the only “primes” of Z〈b〉 are the standard ones). An easy consequence of (1) is that certain induction axioms are satisfied by Z〈b〉. This explains the title of the paper. In the last section of the paper, §3, we shall say more about this.