Dejan E. Lazic

Cryptanalysis of Cryptosystems Based on Remote Chaos Replication

In the last five years, many cryptosystems based on the chaos phenomenon have been proposed. Most of them use chaotic maps, i.e., the discrete-time chaos. The recent announcement of a cryptosystem based on continuous-time chaos that is generated by a very simple electronic circuit known as Chuas circuit passed unrecognized by a large part of the cryptographic community. It is an analog to the VERNAM-cipher system, but uses auto-synchronization through remote replication of the chaotic masking signal. After the introductory description of continuous-time chaotic systems and their synchronization a general definition and discussion of cryptosystems based on remote chaos replication is given. A cryptanalytic attack for these systems is developed that can break the cryptosystem using Chuas circuit for all types of information-bearing signals.

A direct geometrical method for bounding the error exponent for any specific family of channel codes. I. Cutoff rate lower bound for block codes

A direct, general, and conceptually simple geometrical method for determining lower and upper bounds on the error exponent of any specific family of channel block codes is presented. It is considered that a specific family of codes is characterized by a unique distance distribution exponent. The tight linear lower bound of slope -1 on the code family error exponent represents the code family cutoff rate bound. It is always a minimum of a sum of three functions. The intrinsic asymptotic properties of channel block codes are revealed by analyzing these functions and their relationships. It is shown that the random coding technique for lower-bounding the channel error exponent is a special case of this general method. The requirements that a code family should meet in order to have a positive error exponent and at best attain the channel error exponent are stated in a clear way using the (direct) distance distribution method presented. >

Constrained capacity of the AWGN channel

The shortest possible code length of codes on the AWGN channel which attain some prescribed error rate for given code rate and signal-to-noise ratio is considered.

Which Families of Long Binary Lianea Codes Have a Binomial Weight Distribution

In this paper, primitive binary BCH-codes and two linear binary code families based on Hadamard matrices are considered. A review of all results concerning bounds on weight distributions of primitive binary BCH-codes is given in which it is stated that weights of long primitive binary BCH-codes are not binomially distributed. The weight distributions of some particular codes of the last two families are calculated and compared to the values of corresponding binomial distributions. Based on these results the family of binary doubly even self dual codes based on Hadamard matrices seems to be a good candidate to have binomially distributed weights for large code length, i. e., is a good candidate for an asymptotically optimal code family on the binary symmetric channel when decoded by a Maximum-Likelihood-Decoder with all codewords having equal prior probabilities.

On the relation between distance distributions of binary block codes and the binomial distribution

In this paper the impact of the binomial distribution on the behaviour of binary linear and nonlinear block codes is analyzed. Several types of distance distribution of codes and the resulting normalization problems are discussed to enable precise comparisons of distance distributions to the binomial distribution. It is shown that distance distributions of binary linear block codes with rate R ≤ 1 approximate the binomial distribution with an arbitrary precision only if the codes attain the Gilbert-Varshamov bound in the asymptotical case when the code length tends to infinity. From this and some earlier results a new criterion on the optimality of binary linear block codes of finite length is proposed to estimate the quality of these codes on the binary symmetric channel around the cutoff rate when they are decoded by maximum-likelihood decoding. Several codes with their distance distributions are presented and judged according to this new criterion.RésuméDans cet article, on analyse les relations entre la distribution binomiale et le comportement des codes en bloc binaires, linéaires ou non. Plusieurs types de distributions de distances et les problèmes de normalisation qui en decoulent sont exposes pour permettre une comparaison precise de ces distributions avec la distribution binomiale. On montre que la distribution des distances de codes binaires linéaires en bloc de débit R ≤ 1 ne peut approcher la distribution binomiale avec une précision arbitraire que si le code atteint la borne de Gilbert-Varshamov, dans le cas asymptotique où la longueur tend vers ľinfini. On déduit de cela et de résultats antérieurs un nouveau critère ďoptimalité des codes binaires linéaires en bloc de longueur finie, proposé pour estimer la qualité de ces codes sur le canal binaire symétrique au voisinage du débit de coupure quand leur décodage est effectué à vraisemblance maximale. Plusieurs codes, avec la distribution de leurs distances, sont présentés et évalués selon le nouveau critère.

Spectra of long primitive binary BCH codes cannot approach the binomial distribution

Usually spectra (weight distributions) of primitive binary BCH codes are supposed to approximate binomial weight distributions well for a wide range of code rates and code lengths. It is shown that for any fixed code rate R<1 spectra of long (N/spl rarr//spl infin/) primitive binary BCH codes cannot approximate the binomial distribution at all.

Reed-Solomon codes meet the error exponent of the asymptotic uniform symmetric channel

Reed-Solomon codes meet the error exponent of the uniform symmetric channel for all permissible values of the symbol error probability and code rate when the number of channel inputs tends to infinity.

The concatenation error exponent is completely tight

A new lower bound an the error exponent of concatenated codes is derived which coincides with Forneys (1966) upper bound for all code rates.

Necessary and sufficient conditions on codes attaining the channel capacity

Necessary and sufficient conditions on codes attaining the channel capacity in terms of their spectral properties are derived.

Weights of long primitive binary BCH-codes are not binomially distributed

Primitive binary BCH-codes were supposed to have binomial weight distributions for all code rates R/spl les/1 when N/spl rarr//spl infin/. It is shown that this is only true if R/spl rarr/1.