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Affine Coordinate

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Odysseas Koufopavlou – One of the best experts on this subject based on the ideXlab platform.

  • Affine Coordinate Binary Edwards Curve Scalar Multiplier with Side Channel Attack Resistance
    2015 Euromicro Conference on Digital System Design, 2015
    Co-Authors: Apostolos P. Fournaris, Odysseas Koufopavlou

    Abstract:

    Taking into account the high regularity and completeness of Binary Edwards Curves (BEC), BEC point operation efficient implementation in hardware becomes a need especially since such curves tend to be more resistant against side channel attacks than the classical Weierstrass Elliptic Curves. However, BECs require more GF(2k) operations for a single scalar multiplication. This constitutes a deterring factor for their wide adoption and standardization. In this paper, a design methodology, hardware architecture and implementation is proposed on the efficient implementation of BEC scalar multiplication accelerators. To achieve that, a parallelism approach is introduced on Affine Coordinate representation BECs supporting fast GF(2k) inversion through a GF(2k) inversion algorithm capable of realizing also GF(2k) multiplication. The resulting architecture using 4 parallel operating GF(2k) arithmetic units when implemented in FPGA technology provide better results than similar Weierstrass Curves following parallelism techniques, indicated that BECs support parallelism better than their Weierstrass equivalent.

  • DSD – Affine Coordinate Binary Edwards Curve Scalar Multiplier with Side Channel Attack Resistance
    2015 Euromicro Conference on Digital System Design, 2015
    Co-Authors: Apostolos P. Fournaris, Odysseas Koufopavlou

    Abstract:

    Taking into account the high regularity and completeness of Binary Edwards Curves (BEC), BEC point operation efficient implementation in hardware becomes a need especially since such curves tend to be more resistant against side channel attacks than the classical Weierstrass Elliptic Curves. However, BECs require more GF(2k) operations for a single scalar multiplication. This constitutes a deterring factor for their wide adoption and standardization. In this paper, a design methodology, hardware architecture and implementation is proposed on the efficient implementation of BEC scalar multiplication accelerators. To achieve that, a parallelism approach is introduced on Affine Coordinate representation BECs supporting fast GF(2k) inversion through a GF(2k) inversion algorithm capable of realizing also GF(2k) multiplication. The resulting architecture using 4 parallel operating GF(2k) arithmetic units when implemented in FPGA technology provide better results than similar Weierstrass Curves following parallelism techniques, indicated that BECs support parallelism better than their Weierstrass equivalent.

  • ISCAS – Low area Elliptic Curve arithmetic unit
    2009 IEEE International Symposium on Circuits and Systems, 2009
    Co-Authors: Apostolos P. Fournaris, Odysseas Koufopavlou

    Abstract:

    In this paper, a generic Elliptic Curve (EC) arithmetic unit with high flexibility and small chip covered area is proposed. This EC arithmetic unit is based on the one dimensional systolic architectural realization of a proposed modified multiplication – inversion algorithm that through appropriate initialization uses the algorithmic structure of inversion to also perform multiplication. The proposed architecture is realized on FPGA for GF(2163) and is compared with similar up-to-date designs. The proposed EC arithmetic unit has very small chip covered area without any serious penalty in calculation delay and since is designed on the Affine Coordinate plane, it offers a good side channel attack resistance base for further optimizations on this field.

Guangquan Zhang – One of the best experts on this subject based on the ideXlab platform.

  • extension of similarity measures in vsm from orthogonal Coordinate system to Affine Coordinate system
    International Joint Conference on Neural Network, 2014
    Co-Authors: Junyu Xuan, Jie Lu, Guangquan Zhang

    Abstract:

    Similarity measures are the foundations of many research areas, e.g. information retrieval, recommender system and machine learning algorithms. Promoted by these application scenarios, a number of similarity measures have been proposed and proposing. In these state-of-the-art measures, vector-based representation is widely accepted based on Vector Space Model (VSM) in which an object is represented as a vector composed of its features. Then, the similarity between two objects is evaluated by the operations on two corresponding vectors, like cosine, extended jaccard, extended dice and so on. However, there is an assumption that the features are independent of each others. This assumption is apparently unrealistic, and normally, there are relations between features, i.e. the co-occurrence relations between keywords in text mining area. In this paper, a space geometry-based method is proposed to extend the VSM from the orthogonal Coordinate system (OVSM) to Affine Coordinate system (AVSM) and OVSM is proved to be a special case of AVSM. Unit Coordinate vectors of AVSM are inferred by the relations between features which are considered as angles between these unit Coordinate vectors. At last, five different similarity measures are extended from OVSM to AVSM using unit Coordinate vectors of AVSM. Within the numerous application fields of similarity measures, the task of text clustering is selected to be the evaluation criterion. Documents are represented as vectors in OVSM and AVSM, respectively. The clustering results show that AVSM outweighs the OVSM.

  • IJCNN – Extension of similarity measures in VSM: From orthogonal Coordinate system to Affine Coordinate system
    2014 International Joint Conference on Neural Networks (IJCNN), 2014
    Co-Authors: Junyu Xuan, Jie Lu, Guangquan Zhang

    Abstract:

    Similarity measures are the foundations of many research areas, e.g. information retrieval, recommender system and machine learning algorithms. Promoted by these application scenarios, a number of similarity measures have been proposed and proposing. In these state-of-the-art measures, vector-based representation is widely accepted based on Vector Space Model (VSM) in which an object is represented as a vector composed of its features. Then, the similarity between two objects is evaluated by the operations on two corresponding vectors, like cosine, extended jaccard, extended dice and so on. However, there is an assumption that the features are independent of each others. This assumption is apparently unrealistic, and normally, there are relations between features, i.e. the co-occurrence relations between keywords in text mining area. In this paper, a space geometry-based method is proposed to extend the VSM from the orthogonal Coordinate system (OVSM) to Affine Coordinate system (AVSM) and OVSM is proved to be a special case of AVSM. Unit Coordinate vectors of AVSM are inferred by the relations between features which are considered as angles between these unit Coordinate vectors. At last, five different similarity measures are extended from OVSM to AVSM using unit Coordinate vectors of AVSM. Within the numerous application fields of similarity measures, the task of text clustering is selected to be the evaluation criterion. Documents are represented as vectors in OVSM and AVSM, respectively. The clustering results show that AVSM outweighs the OVSM.

J Ohya – One of the best experts on this subject based on the ideXlab platform.

  • Novel scene generation, merging and stitching views using the 2D Affine space
    Signal Processing-image Communication, 1998
    Co-Authors: K Sengupta, J Ohya

    Abstract:

    In this paper we present a unified theoretical framework for novel scene synthesis, merging real and virtual worlds, and view stitching. To start with, we have a set of real images from weakly calibrated cameras, for which we compute the dense point match correspondences. For applications like novel view synthesis, one may first solve the 3D scene reconstruction problem, followed by a view rendering process. However, errors in 3D scene reconstruction usually gets reflected in the quality of the new scene generated, so we seek a more direct method. In this paper, we use the knowledge of dense point matches and their Affine Coordinate values to estimate the corresponding Affine Coordinate values in the new scene. Our technique of reprojection is extended for other applications like merging real and synthetic worlds, and view stitching.

  • an Affine Coordinate based algorithm for reprojecting the human face for identification tasks
    International Conference on Image Processing, 1997
    Co-Authors: K Sengupta, J Ohya

    Abstract:

    We present an algorithm to generate new views of a human face, starting with at least two other views of the face. In a typical face recognition system, the task of comparison becomes easier if the faces have similar orientation with respect to the camera. The Affine Coordinate based reprojection algorithm presented enables us to do that. Dense point matches between the two input faces of the same individual are computed using an Affine Coordinate based reprojection framework. This is followed by the reprojection of one of these to faces to the target face once the user has matched four feature points across two input face images and the target face image.

  • ICIP (3) – An Affine Coordinate based algorithm for reprojecting the human face for identification tasks
    Proceedings of International Conference on Image Processing, 1
    Co-Authors: K Sengupta, J Ohya

    Abstract:

    We present an algorithm to generate new views of a human face, starting with at least two other views of the face. In a typical face recognition system, the task of comparison becomes easier if the faces have similar orientation with respect to the camera. The Affine Coordinate based reprojection algorithm presented enables us to do that. Dense point matches between the two input faces of the same individual are computed using an Affine Coordinate based reprojection framework. This is followed by the reprojection of one of these to faces to the target face once the user has matched four feature points across two input face images and the target face image.