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        "author": "Homer Hsing",
        "author_email": "homer.hsing@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 5 - Production/Stable",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: GNU Library or Lesser General Public License (LGPL)",
            "Operating System :: OS Independent",
            "Programming Language :: Python",
            "Topic :: Scientific/Engineering :: Mathematics"
        ],
        "description": "Introduction\n\nThis package is a Python library for calculating Tate bilinear pairing, \nespecially on super-singular elliptic curve $E:y^2=x^3-x+1$ in affine \ncoordinates defined over a Galois Field $GF(3^m)$. The largest order of \n$G_1$ is 911 bits.\n\nThis package is also for calculating the addition of two elements \nin the elliptic curve group, and the addition of $k$ identical element \nin the elliptic curve group.\n\nThe code of this package for computing the Tate bilinear pairing follows \nthe paper by Beuchat et al [3]. The code of this package for computing \nthe elliptic curve group operation follows the paper by Kerins et al [2].\n\nThis package is in PURE Python, working with Python 2.7 and 3.2.\n\nThis package computes one Tate bilinear pairing within 3.26 seconds \n@ Intel Core2 L7500 CPU (1.60GHz) if the order of $G_1$ is 151 bits.\n\n=================================================\n\nWhat is Tate bilinear pairing\n\nGenerally speaking, The Tate bilinear pairing algorithm is a transformation \nthat takes two points on an elliptic curve and outputs a nonzero element \nin the extension field $GF(3^{6m})$. The state-of-the-art way of computing \nthe Tate bilinear pairing is eta pairing, introduced by Barreto et al [4]. \nFor more information, please refer to [1,2,3,4].\n\n=================================================\n\nUsage 1: calculating Tate bilinear pairing\n\nSpecify the order of G1 is of 151 bits:\n\n>>> from tate_bilinear_pairing import eta\n>>> eta.init(151)\n\nGiven two random numbers like this:\n\n>>> import random\n>>> a = random.randint(0,1000)\n>>> b = random.randint(0,1000)\n\nComputing two elements $[inf1, x1, y1]$, and $[inf2, x2, y2]$ in \nthe elliptic curve group:\n\n>>> from tate_bilinear_pairing import ecc\n>>> g = ecc.gen()\n>>> inf1, x1, y1 = ecc.scalar_mult(a, g)\n>>> inf2, x2, y2 = ecc.scalar_mult(b, g)\n\nTate bilinear pairing is done via:\n\n>>> from tate_bilinear_pairing import eta\n>>> t = eta.pairing(x1, y1, x2, y2)\n\n=================================================\n\nUsage 2: calculating the addition of two elements in the elliptic curve group\n\nGiven two elements $p1=[inf1, x1, y1]$, and $p2=[inf2, x2, y2]$ in the \nelliptic curve group, the addition is done via:\n\n>>> p1 = [inf1, x1, y1]\n>>> p2 = [inf2, x2, y2]\n>>> p3 = ecc.add(p1, p2)\n\n=================================================\n\nUsage 3: calculating the addition of $k$ identical elements\n\nGiven a non-negative integer $k$ and an group element $p1=[inf1, x1, y1]$, \n$k \\cdot p1$ is computed via:\n\n>>> k = random.randint(0,1000)\n>>> p3 = ecc.scalar_mult(k, p1)\n\n=================================================\n\nReferences\n\n[1] I. Duursma, H.S. Lee. \n    Tate pairing implementation for hyper-elliptic curves $y^2=x^p-x+d$.\n    Advances in Cryptology - Proc. ASIACRYPT \u201903, pp. 111-123, 2003.\n[2] T. Kerins, W.P. Marnane, E.M. Popovici, and P.S.L.M. Barreto.\n    Efficient hardware for the Tate pairing calculation in characteristic three.\n    Cryptographic Hardware and Embedded Systems - Proc. CHES \u201905, pp. 412-426, 2005.\n[3] J. Beuchat, N. Brisebarre, J. Detrey, E. Okamoto, M. Shirase, and T. Takagi. \n    Algorithms and Arithmetic Operators for Computing the $\\eta_T$ Pairing in Characteristic Three.\n    IEEE Transactions on Computers, Special Section on Special-Purpose Hardware for Cryptography and Cryptanalysis, vol. 57 no. 11 pp. 1454-1468, 2008.\n[4] P.S.L.M. Barreto, S.D. Galbraith, C. O hEigeartaigh, and M. Scott,\n    Efficient Pairing Computation on Supersingular Abelian Varieties.\n    Designs, Codes and Cryptography, vol. 42, no. 3, pp. 239-271, Mar. 2007.",
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