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Kittiphon Phalakarn - One of the best experts on this subject based on the ideXlab platform.

  • optimal Representation for right to left parallel scalar and multi scalar point multiplication
    International journal of networking and computing, 2018
    Co-Authors: Kittiphon Phalakarn, Vorapong Suppakitpaisarn
    Abstract:

    This paper introduces an optimal Representation for a right-to-left parallel elliptic curve scalar point multiplication. The right-to-left approach is easier to parallelize than the Conventional left-to-right approach. However, unlike the left-to-right approach, there is still no work considering number Representations for the right-to-left parallel calculation. By simplifying the implementation by Robert, we devise a mathematical model to capture the computation time of the calculation. Then, for any arbitrary amount of doubling time and addition time, we propose algorithms to generate Representations which minimize the time in that model. As a result, we can show a negative result that a Conventional Representation like NAF is almost optimal. The parallel computation time obtained from any Representation cannot be better than NAF by more than 1%. In addition to that, we devise a time model and propose an algorithm to generate optimal Representations for multi-scalar point multiplication (under a condition). Similar to the result of scalar point multiplication, NAF is almost optimal also for multi-scalar point multiplication as the difference of parallel computation time obtained from optimal Representation and NAF is less than 1% in all experimental settings.

  • optimal Representation for right to left parallel scalar point multiplication
    International Symposium on Computing and Networking, 2017
    Co-Authors: Kittiphon Phalakarn, Vorapong Suppakitpaisarn
    Abstract:

    This paper introduces an optimal Representation for a right-to-left parallel elliptic curve scalar point multiplication. The right-to-left approach is easier to parallelize than the Conventional left-to-right approach. However, unlike the left-to-right approach, there is still no work considering number Representations for the right-to-left parallel calculation. By simplifying the implementation by Robert, we devise a mathematical model to capture the computation time of the calculation. Then, for any arbitrary amount of doubling time and addition time, we propose algorithms to generate Representations which minimize the time in that model. As a result, we can show a negative result that a Conventional Representation like NAF is almost optimal. The parallel computation time obtained from any Representation cannot be better than NAF by more than 1%.

Vorapong Suppakitpaisarn - One of the best experts on this subject based on the ideXlab platform.

  • optimal Representation for right to left parallel scalar and multi scalar point multiplication
    International journal of networking and computing, 2018
    Co-Authors: Kittiphon Phalakarn, Vorapong Suppakitpaisarn
    Abstract:

    This paper introduces an optimal Representation for a right-to-left parallel elliptic curve scalar point multiplication. The right-to-left approach is easier to parallelize than the Conventional left-to-right approach. However, unlike the left-to-right approach, there is still no work considering number Representations for the right-to-left parallel calculation. By simplifying the implementation by Robert, we devise a mathematical model to capture the computation time of the calculation. Then, for any arbitrary amount of doubling time and addition time, we propose algorithms to generate Representations which minimize the time in that model. As a result, we can show a negative result that a Conventional Representation like NAF is almost optimal. The parallel computation time obtained from any Representation cannot be better than NAF by more than 1%. In addition to that, we devise a time model and propose an algorithm to generate optimal Representations for multi-scalar point multiplication (under a condition). Similar to the result of scalar point multiplication, NAF is almost optimal also for multi-scalar point multiplication as the difference of parallel computation time obtained from optimal Representation and NAF is less than 1% in all experimental settings.

  • optimal Representation for right to left parallel scalar point multiplication
    International Symposium on Computing and Networking, 2017
    Co-Authors: Kittiphon Phalakarn, Vorapong Suppakitpaisarn
    Abstract:

    This paper introduces an optimal Representation for a right-to-left parallel elliptic curve scalar point multiplication. The right-to-left approach is easier to parallelize than the Conventional left-to-right approach. However, unlike the left-to-right approach, there is still no work considering number Representations for the right-to-left parallel calculation. By simplifying the implementation by Robert, we devise a mathematical model to capture the computation time of the calculation. Then, for any arbitrary amount of doubling time and addition time, we propose algorithms to generate Representations which minimize the time in that model. As a result, we can show a negative result that a Conventional Representation like NAF is almost optimal. The parallel computation time obtained from any Representation cannot be better than NAF by more than 1%.

Sheshukov A. - One of the best experts on this subject based on the ideXlab platform.

  • Dynamic capillary pressure mechanism for instability in gravity-driven flows; review and extension to very dry conditions
    2020
    Co-Authors: Nieber J., Dautov R., Egorov A., Sheshukov A.
    Abstract:

    Several alternative mathematical models for describing water flow in unsaturated porous media are presented. These models are based on an equation for conservation of mass of water, and a generalized linear law for water flux (Darcy's law) containing a term called the dynamic capillary pressure. The distinct form of each alternative model is based on the specific form of expression used to describe the dynamic capillary pressure. The Conventional Representation arises when this pressure is set equal to the equilibrium pressure given by the capillary pressure - saturation function for unsaturated porous media, and this Conventional approach leads to the Richards equation. Other models are derived by representing the dynamic capillary pressure by a rheological relationship stating that the pressure is not given directly by the capillary pressure - saturation function. Two forms of rheological relationship are considered in this manuscript, a very general non-equilibrium relation, and a more specific relation expressed by a first-order kinetic equation referred to as a relaxation relation. For the general non-equilibrium relation the system of governing equations is called the general Non-Equilibrium Richards Equation (NERE), and for the case of the relaxation relation the system is called the Relaxation Non-Equilibrium Richards Equation (RNERE). Each of the alternative models was analyzed for flow characteristics under gravity-dominant conditions by using a traveling wave transformation for the model equations, and more importantly the flow described by each model was analyzed for linear stability. It is shown that when a flow field is perturbed by infinitesimal disturbances, the RE is unconditionally stable, while both the NERE and the RNERE are conditionally stable. The stability analysis for the NERE was limited to disturbances in the very low frequency range because of the general form of the NERE model. This analysis resulted in what we call a low-frequency criterion (LFC) for stability. This LFC is also shown to apply to the stability of the RE and the RNERE. The LFC is applied to stability analysis of the RNERE model for conditions of initial saturation less than residual. © Springer 2005

Aleksey Y Sheshukov - One of the best experts on this subject based on the ideXlab platform.

  • dynamic capillary pressure mechanism for instability in gravity driven flows review and extension to very dry conditions
    Transport in Porous Media, 2005
    Co-Authors: John L Nieber, R Z Dautov, A G Egorov, Aleksey Y Sheshukov
    Abstract:

    Several alternative mathematical models for describing water flow in unsaturated porous media are presented. These models are based on an equation for conservation of mass of water, and a generalized linear law for water flux (Darcy’s law) containing a term called the dynamic capillary pressure. The distinct form of each alternative model is based on the specific form of expression used to describe the dynamic capillary pressure. The Conventional Representation arises when this pressure is set equal to the equilibrium pressure given by the capillary pressure -- saturation function for unsaturated porous media, and this Conventional approach leads to the Richards equation. Other models are derived by representing the dynamic capillary pressure by a rheological relationship stating that the pressure is not given directly by the capillary pressure -- saturation function. Two forms of rheological relationship are considered in this manuscript, a very general non-equilibrium relation, and a more specific relation expressed by a first-order kinetic equation referred to as a relaxation relation. For the general non-equilibrium relation the system of governing equations is called the general Non-Equilibrium Richards Equation (NERE), and for the case of the relaxation relation the system is called the Relaxation Non-Equilibrium Richards Equation (RNERE). Each of the alternative models was analyzed for flow characteristics under gravity-dominant conditions by using a traveling wave transformation for the model equations, and more importantly the flow described by each model was analyzed for linear stability. It is shown that when a flow field is perturbed by infinitesimal disturbances, the RE is unconditionally stable, while both the NERE and the RNERE are conditionally stable. The stability analysis for the NERE was limited to disturbances in the very low frequency range because of the general form of the NERE model. This analysis resulted in what we call a low-frequency criterion (LFC) for stability. This LFC is also shown to apply to the stability of the RE and the RNERE. The LFC is applied to stability analysis of the RNERE model for conditions of initial saturation less than residual.

Nieber J. - One of the best experts on this subject based on the ideXlab platform.

  • Dynamic capillary pressure mechanism for instability in gravity-driven flows; review and extension to very dry conditions
    2020
    Co-Authors: Nieber J., Dautov R., Egorov A., Sheshukov A.
    Abstract:

    Several alternative mathematical models for describing water flow in unsaturated porous media are presented. These models are based on an equation for conservation of mass of water, and a generalized linear law for water flux (Darcy's law) containing a term called the dynamic capillary pressure. The distinct form of each alternative model is based on the specific form of expression used to describe the dynamic capillary pressure. The Conventional Representation arises when this pressure is set equal to the equilibrium pressure given by the capillary pressure - saturation function for unsaturated porous media, and this Conventional approach leads to the Richards equation. Other models are derived by representing the dynamic capillary pressure by a rheological relationship stating that the pressure is not given directly by the capillary pressure - saturation function. Two forms of rheological relationship are considered in this manuscript, a very general non-equilibrium relation, and a more specific relation expressed by a first-order kinetic equation referred to as a relaxation relation. For the general non-equilibrium relation the system of governing equations is called the general Non-Equilibrium Richards Equation (NERE), and for the case of the relaxation relation the system is called the Relaxation Non-Equilibrium Richards Equation (RNERE). Each of the alternative models was analyzed for flow characteristics under gravity-dominant conditions by using a traveling wave transformation for the model equations, and more importantly the flow described by each model was analyzed for linear stability. It is shown that when a flow field is perturbed by infinitesimal disturbances, the RE is unconditionally stable, while both the NERE and the RNERE are conditionally stable. The stability analysis for the NERE was limited to disturbances in the very low frequency range because of the general form of the NERE model. This analysis resulted in what we call a low-frequency criterion (LFC) for stability. This LFC is also shown to apply to the stability of the RE and the RNERE. The LFC is applied to stability analysis of the RNERE model for conditions of initial saturation less than residual. © Springer 2005