A General Zero-Knowledge Scheme

There is a great similarity between the zero-knowledge proof of quadratic residuocity presented by Goldwasser-Micali-Rackoff and the graph isomorphism proof presented by Goldreich-Micali-Wigderson. There is also a resemblance between the zero-knowledge proofs of Fiat-Shamir, Chaum-Evertse-van de Graaf, Beth and Guillou-Quisquater. A similar observation holds for zero-knowledge proofs based on encryption: the 3-colourability proofs and the Hamiltonian-circuit proofs of Blum and Goldreich-Micali-Wigderson, and the Brassard-Chaum-Crepeau proof for SAT. Feige, Fiat and Shamir introduced the concept of zero-knowledge proofs of knowledge. In this paper we present a general zero-knowledge scheme which unifies all these Arthur-Merlin proofs.     

Run distribution innonlinear binary generators

In this work, an easy method of computing the exact number of runs of ones and zerosin the sequence obtained from LFSR-based nonlinear generators has been developed. The procedure is based on the decomposition of the generating function in global minterms. If the obtained results are not in the expected range, then the sequence generator must be rejected for cryptographic purposes.     

Hypergraph decomposition and secret sharing

A secret sharing scheme is a protocol by which a dealer distributes a secret among a set of participants in such a way that only qualified sets of them can reconstruct the value of the secret whereas any non-qualified subset of participants obtain no information at all about the value of the secret. Secret sharing schemes have always played a very important role for cryptographic applications and in the construction of higher level cryptographic primitives and protocols.In this paper we investigate the construction of efficient secret sharing schemes by using a technique called hypergraph decomposition, extending in a non-trivial way the previously studied graph decomposition techniques. A major advantage of hypergraph decomposition is that it applies to any access structure, rather than only structures representable as graphs. As a consequence, the application of this technique allows us to obtain secret sharing schemes for several classes of access structures (such as hyperpaths, hypercycles, hyperstars and acyclic hypergraphs) with improved efficiency over previous results. Specifically, for these access structures, we present secret sharing schemes that achieve optimal information rate. Moreover, with respect to the average information rate, our schemes improve on previously known ones.In the course of the formulation of the hypergraph decomposition technique, we also obtain an elementary characterization of the ideal access structures among the hyperstars, which is of independent interest.     

Asymptotic Nonlinearity of Boolean Functions

Boolean functions on the space are not only important in the theory of error-correcting codes, but also in cryptography. In these two cases, the nonlinearity of these functions is a main concept. Carlet, Olejár and Stanek gave an asymptotic lower bound for the nonlinearity of most of them, and I gave an asymptotic upper bound which was strictly larger. In this article, I improve the bounds and get an exact limit for the nonlinearity of most of Boolean functions. This article is inspired by a paper of G. Halász about the related problem of real polynomials with random coefficients. AMS Classification (2000) Primary: 11T71 · Secondary: 06E30 · 42A05 · 94C10     

A chaos secure communication scheme based on multiplication modulation

A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.     

On hiding messages in the oversampled Fourier coefficients

A system using an oversampled Fourier transform for hiding data is given in [J.R. Miotke, L. Rebollo-Neira, Oversampling of Fourier coefficients for hiding messages, Appl. Comput. Harmon. Anal. 16 (2004) 203-207]. When viewed as a cryptographic algorithm, we demonstrate here that the system is susceptible to a known plaintext attack.     

Combinatorial Classification of Optimal Authentication Codes with Arbitration

Unconditionallysecure authentication codes with arbitration ( A ²-codes)protect against deceptions from the transmitter and the receiveras well as that from the opponent. We first show that an optimalA ²-code implies an orthogonal array and an affine-resolvable design. Next we define a new design,an affine -resolvable + BIBD,and prove that optimal A ²-codes are equivalentto this new design. From this equivalence, we derive a conditionon the parameters for the existence of optimal A ²-codes.Further, we show tighter lower bounds on the size of keys thanbefore for large sizes of source states which can be consideredas an extension of the bounds on the related designs.     

Isomorphism classes of Doche–Icart–Kohel curves over finite fields

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in two families of curves introduced by C. Doche, T. Icart and D.R. Kohel.     

A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption

A novel and robust chaos-based pseudorandom permutation-substitution scheme for image encryption is proposed. It is a loss-less symmetric block cipher and specifically designed for the color images but may also be used for the gray scale images. A secret key of 161-bit, comprising of the initial conditions and system parameter of the chaotic map (the standard map), number of iterations and number of rounds, is used in the algorithm. The whole encryption process is the sequential execution of a preliminary permutation and a fix number of rounds (as specified in the secret key) of substitution and main permutation of the 2D matrix obtained from the 3D image matrix. To increase the speed of encryption all three processes: preliminary permutation, substitution and main permutation are done row-by-row and column-by-column instead of pixel-by-pixel. All the permutation processes are made dependent on the input image matrix and controlled through the pseudo random number sequences (PRNS) generated from the discretization of chaotic standard map which result in both key sensitivity and plaintext sensitivity. However each substitution process is initiated with the initial vectors (different for rows and columns) generated using the secret key and chaotic standard map and then the properties of rows and column pixels of input matrix are mixed with the PRNS generated from the standard map. The security and performance analysis of the proposed image encryption has been performed using the histograms, correlation coefficients, information entropy, key sensitivity analysis, differential analysis, key space analysis, encryption/decryption rate analysis etc. Results suggest that the proposed image encryption technique is robust and secure and can be used for the secure image and video communication applications.     

Discrete chaotic cryptography

In the paper we propose a new method of constructing cryptosystems utilising a nonpredictability property of discrete chaotic systems. We formulate the requirements for such systems to assure their safety. We also give examples of practical realisation of chaotic cryptosystems, using a generalisation of the method presented in [7]. The proposed algorithm of encryption and decryption is based on multiple iteration of a certain dynamical chaotic system. We assume that some part of the initial condition is a plain message. As the secret key we assume the system parameter(s) and additionally another part of the initial condition.