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Alexander Pott - One of the best experts on this subject based on the ideXlab platform.
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on designs and multiplier groups constructed from almost perfect Nonlinear Functions
2009Co-Authors: Yves Edel, Alexander PottAbstract:Let $f:{\mathbb{F}_2^{n}}\to {\mathbb{F}_2^{n}}$ be an almost perfect Nonlinear Function (APN). The set $D_f:=\{(a,b)\: :\: f(x+a)-f(x)=b\mbox{\ has two solutions}\}$ can be used to distinguish APN Functions up to equivalence. We investigate the multiplier groups of theses sets D f . This extends earlier work done by the authors [1].
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a new almost perfect Nonlinear Function which is not quadratic
2009Co-Authors: Yves Edel, Alexander PottAbstract:Following an example in [12], we show how to change one coordinate Function of an almost perfect Nonlinear (APN) Function in order to obtain new examples. It turns out that this is a very powerful method to construct new APN Functions. In particular, we show that our approach can be used to construct a ''non-quadratic'' APN Function. This new example is in remarkable contrast to all recently constructed Functions which have all been quadratic. An equivalent Function has been found independently by Brinkmann and Leander [8]. However, they claimed that their Function is CCZ equivalent to a quadratic one. In this paper we give several reasons why this new Function is not equivalent to a quadratic one.
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a new almost perfect Nonlinear Function which is not quadratic
2008Co-Authors: Yves Edel, Alexander PottAbstract:Following an example in [13], we show how to change one coordinate Function of an almost perfect Nonlinear (APN) Function in order to obtain new examples. It turns out that this is a very powerful method to construct new APN Functions. In particular, we show that the approach can be used to construct “non-quadratic” APN Functions. This new example is in remarkable contrast to all recently constructed Functions which have all been quadratic. 1 Preliminaries In this paper, we consider Functions F : F n 2 → F n 2 with “good” differential and linear properties. Motivated by applications in cryptography, a lot of research has been done to construct Functions which are “as Nonlinear as possible”. We discuss two possibilities to define Nonlinearity: One approach uses differential properties of linear Functions, the other measures the “distance” to linear Functions. Let us begin with the differential properties. Given F : F n 2 → F n 2 , we define ∆F (a, b) := |{x : F (x+ a)− F (x) = b}|. We have ∆F (0, 0) = 2 , and ∆F (0, b) = 0 if b 6= 0. Since we are working in fields of characteristic 2, we may replace the “−” by + and write F (x+a)+F (x) instead of F (x−a)−F (x). We say that F is almost perfect Nonlinear (APN) if ∆F (a, b) ∈ {0, 2} for all a, b ∈ F n 2 , a 6= 0. Note that ∆F (a, b) ∈ {0, 2} if F is linear, hence the condition ∆F (a, b) ∈ {0, 2} identifies Functions which are quite different from linear mappings. Since we are working in characteristic 2, it is impossible that ∆F (a, b) = 1 for some a, b, since the values ∆F (a, b) must be even: If x is a solution of F (x + a)− F (x) = b, then x + a, too. In the case of odd characteristic, Functions F : F n q → F n q with ∆F (a, b) = 1 for all a 6= 0 do exist, and they are called perfect Nonlinear or planar. In the last few years, many new APN Functions have been constructed. The first example of a non-power mapping has been described in [26]. Infinite series are contained in [5, 10, 11, 12, 13, 16, 17]. Also some new planar Functions have been found, see [15, 22, 36]. There may be a possibility for a unified treatment of (some of) these constructions in the even and odd characteristic case. In particular, we suggest to look more carefully at the underlying design of an APN Function, similar to the designs corresponding to planar Functions, which are projective planes, see [29]. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, B-9000 Ghent, Belgium. The research is supported by the Interuniversitary Attraction Poles Programme-Belgian State-Belgian Science Policy: project P6/26-Bcrypt. Department of Mathematics, Otto-von-Guericke-University Magdeburg, D-39016 Magdeburg, Germany An equivalent Function has been found independently by Brinkmann and Leander [7]. However, they claimed that their Function is CCZ equivalent to a quadratic one. In this paper we give several reasons why this new Function is not equivalent to a quadratic one
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a new apn Function which is not equivalent to a power mapping
2006Co-Authors: Yves Edel, Gohar M Kyureghyan, Alexander PottAbstract:A new almost-perfect Nonlinear Function (APN) on F(2/sup 10/) which is not equivalent to any of the previously known APN mappings is constructed. This is the first example of an APN mapping which is not equivalent to a power mapping.
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a new apn Function which is not equivalent to a power mapping
2005Co-Authors: Yves Edel, Gohar M Kyureghyan, Alexander PottAbstract:A new almost perfect Nonlinear Function (APN) on the finite field GF(2^10) which is not equivalent to any of the previously known APN mappings is constructed. This is the first example of an APN mapping which is not equivalent to a power mapping.
Yves Edel - One of the best experts on this subject based on the ideXlab platform.
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on designs and multiplier groups constructed from almost perfect Nonlinear Functions
2009Co-Authors: Yves Edel, Alexander PottAbstract:Let $f:{\mathbb{F}_2^{n}}\to {\mathbb{F}_2^{n}}$ be an almost perfect Nonlinear Function (APN). The set $D_f:=\{(a,b)\: :\: f(x+a)-f(x)=b\mbox{\ has two solutions}\}$ can be used to distinguish APN Functions up to equivalence. We investigate the multiplier groups of theses sets D f . This extends earlier work done by the authors [1].
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a new almost perfect Nonlinear Function which is not quadratic
2009Co-Authors: Yves Edel, Alexander PottAbstract:Following an example in [12], we show how to change one coordinate Function of an almost perfect Nonlinear (APN) Function in order to obtain new examples. It turns out that this is a very powerful method to construct new APN Functions. In particular, we show that our approach can be used to construct a ''non-quadratic'' APN Function. This new example is in remarkable contrast to all recently constructed Functions which have all been quadratic. An equivalent Function has been found independently by Brinkmann and Leander [8]. However, they claimed that their Function is CCZ equivalent to a quadratic one. In this paper we give several reasons why this new Function is not equivalent to a quadratic one.
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a new almost perfect Nonlinear Function which is not quadratic
2008Co-Authors: Yves Edel, Alexander PottAbstract:Following an example in [13], we show how to change one coordinate Function of an almost perfect Nonlinear (APN) Function in order to obtain new examples. It turns out that this is a very powerful method to construct new APN Functions. In particular, we show that the approach can be used to construct “non-quadratic” APN Functions. This new example is in remarkable contrast to all recently constructed Functions which have all been quadratic. 1 Preliminaries In this paper, we consider Functions F : F n 2 → F n 2 with “good” differential and linear properties. Motivated by applications in cryptography, a lot of research has been done to construct Functions which are “as Nonlinear as possible”. We discuss two possibilities to define Nonlinearity: One approach uses differential properties of linear Functions, the other measures the “distance” to linear Functions. Let us begin with the differential properties. Given F : F n 2 → F n 2 , we define ∆F (a, b) := |{x : F (x+ a)− F (x) = b}|. We have ∆F (0, 0) = 2 , and ∆F (0, b) = 0 if b 6= 0. Since we are working in fields of characteristic 2, we may replace the “−” by + and write F (x+a)+F (x) instead of F (x−a)−F (x). We say that F is almost perfect Nonlinear (APN) if ∆F (a, b) ∈ {0, 2} for all a, b ∈ F n 2 , a 6= 0. Note that ∆F (a, b) ∈ {0, 2} if F is linear, hence the condition ∆F (a, b) ∈ {0, 2} identifies Functions which are quite different from linear mappings. Since we are working in characteristic 2, it is impossible that ∆F (a, b) = 1 for some a, b, since the values ∆F (a, b) must be even: If x is a solution of F (x + a)− F (x) = b, then x + a, too. In the case of odd characteristic, Functions F : F n q → F n q with ∆F (a, b) = 1 for all a 6= 0 do exist, and they are called perfect Nonlinear or planar. In the last few years, many new APN Functions have been constructed. The first example of a non-power mapping has been described in [26]. Infinite series are contained in [5, 10, 11, 12, 13, 16, 17]. Also some new planar Functions have been found, see [15, 22, 36]. There may be a possibility for a unified treatment of (some of) these constructions in the even and odd characteristic case. In particular, we suggest to look more carefully at the underlying design of an APN Function, similar to the designs corresponding to planar Functions, which are projective planes, see [29]. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, B-9000 Ghent, Belgium. The research is supported by the Interuniversitary Attraction Poles Programme-Belgian State-Belgian Science Policy: project P6/26-Bcrypt. Department of Mathematics, Otto-von-Guericke-University Magdeburg, D-39016 Magdeburg, Germany An equivalent Function has been found independently by Brinkmann and Leander [7]. However, they claimed that their Function is CCZ equivalent to a quadratic one. In this paper we give several reasons why this new Function is not equivalent to a quadratic one
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a new apn Function which is not equivalent to a power mapping
2006Co-Authors: Yves Edel, Gohar M Kyureghyan, Alexander PottAbstract:A new almost-perfect Nonlinear Function (APN) on F(2/sup 10/) which is not equivalent to any of the previously known APN mappings is constructed. This is the first example of an APN mapping which is not equivalent to a power mapping.
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a new apn Function which is not equivalent to a power mapping
2005Co-Authors: Yves Edel, Gohar M Kyureghyan, Alexander PottAbstract:A new almost perfect Nonlinear Function (APN) on the finite field GF(2^10) which is not equivalent to any of the previously known APN mappings is constructed. This is the first example of an APN mapping which is not equivalent to a power mapping.
Li Deng - One of the best experts on this subject based on the ideXlab platform.
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adaptive kalman filtering and smoothing for tracking vocal tract resonances using a continuous valued hidden dynamic model
2007Co-Authors: Li Deng, Leo J Lee, Hagai Attias, Alejandro AceroAbstract:A novel Kalman filtering/smoothing algorithm is presented for efficient and accurate estimation of vocal tract resonances or formants, which are natural frequencies and bandwidths of the resonator from larynx to lips, in fluent speech. The algorithm uses a hidden dynamic model, with a state-space formulation, where the resonance frequency and bandwidth values are treated as continuous-valued hidden state variables. The observation equation of the model is constructed by an analytical predictive Function from the resonance frequencies and bandwidths to LPC cepstra as the observation vectors. This Nonlinear Function is adaptively linearized, and a residual or bias term, which is adaptively trained, is added to the Nonlinear Function to represent the iteratively reduced piecewise linear approximation error. Details of the piecewise linearization design process are described. An iterative tracking algorithm is presented, which embeds both the adaptive residual training and piecewise linearization design in the Kalman filtering/smoothing framework. Experiments on estimating resonances in Switchboard speech data show accurate estimation results. In particular, the effectiveness of the adaptive residual training is demonstrated. Our approach provides a solution to the traditional "hidden formant problem," and produces meaningful results even during consonantal closures when the supra-laryngeal source may cause no spectral prominences in speech acoustics
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tracking vocal tract resonances using a quantized Nonlinear Function embedded in a temporal constraint
2006Co-Authors: Li Deng, Alex Acero, I BazziAbstract:This paper presents a new technique for high-accuracy tracking of vocal-tract resonances (which coincide with formants for nonnasalized vowels) in natural speech. The technique is based on a discretized Nonlinear prediction Function, which is embedded in a temporal constraint on the quantized input values over adjacent time frames as the prior knowledge for their temporal behavior. The Nonlinear prediction is constructed, based on its analytical form derived in detail in this paper, as a parameter-free, discrete mapping Function that approximates the “forward” relationship from the resonance frequencies and bandwidths to the Linear Predictive Coding (LPC) cepstra of real speech. Discretization of the Function permits the “inversion” of the Function via a search operation. We further introduce the Nonlinear-prediction residual, characterized by a multivariate Gaussian vector with trainable mean vectors and covariance matrices, to account for the errors due to the Functional approximation. We develop and describe an expectation–maximization (EM)-based algorithm for training the parameters of the residual, and a dynamic programming-based algorithm for resonance tracking. Details of the algorithm implementation for computation speedup are provided. Experimental results are presented which demonstrate the effectiveness of our new paradigm for tracking vocal-tract resonances. In particular, we show the effectiveness of training the prediction-residual parameters in obtaining high-accuracy resonance estimates, especially during consonantal closure.
I Bazzi - One of the best experts on this subject based on the ideXlab platform.
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tracking vocal tract resonances using a quantized Nonlinear Function embedded in a temporal constraint
2006Co-Authors: Li Deng, Alex Acero, I BazziAbstract:This paper presents a new technique for high-accuracy tracking of vocal-tract resonances (which coincide with formants for nonnasalized vowels) in natural speech. The technique is based on a discretized Nonlinear prediction Function, which is embedded in a temporal constraint on the quantized input values over adjacent time frames as the prior knowledge for their temporal behavior. The Nonlinear prediction is constructed, based on its analytical form derived in detail in this paper, as a parameter-free, discrete mapping Function that approximates the “forward” relationship from the resonance frequencies and bandwidths to the Linear Predictive Coding (LPC) cepstra of real speech. Discretization of the Function permits the “inversion” of the Function via a search operation. We further introduce the Nonlinear-prediction residual, characterized by a multivariate Gaussian vector with trainable mean vectors and covariance matrices, to account for the errors due to the Functional approximation. We develop and describe an expectation–maximization (EM)-based algorithm for training the parameters of the residual, and a dynamic programming-based algorithm for resonance tracking. Details of the algorithm implementation for computation speedup are provided. Experimental results are presented which demonstrate the effectiveness of our new paradigm for tracking vocal-tract resonances. In particular, we show the effectiveness of training the prediction-residual parameters in obtaining high-accuracy resonance estimates, especially during consonantal closure.
Junxi Sun - One of the best experts on this subject based on the ideXlab platform.
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blind speech separation employing laplacian normal mixture distribution model
2007Co-Authors: Hua Cai, Junxi SunAbstract:Careful choice of Nonlinear Function is necessary to obtain good performance from algorithms for blind source separation. In this paper, we propose a fast approach to perform blind speech separation based on natural gradient. The main ingredient is the use of a novel Nonlinear Function, which is accordant to the true PDF of speech signals. By appropriately choosing the shape parameter, we approximate a Laplacian normal mixture distribution to the source's PDF in time domain, then a new form of Nonlinear Function more suitable for speech separation is derived using the given distribution model. Simulation results indicate the good convergence and steady-state performance of our proposed method.
