{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "use sage" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Prerequisites\n", "- Elliptic curves\n", "\n", "**Reminder** \n", "Weierstrass curve\n", "$$y^2 = x^3 + ax + b$$\n", "with $4a^3 + 27b^2 \\neq 0$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Theory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The unit circle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the unit circle\n", "$$y^2 + x^2 = 1$$\n", "\n", "And consider an addition law being addition on angles as follows:\n", "$$\\sin(\\alpha_1 + \\alpha_2) = \\sin \\alpha_1 \\cos \\alpha_2 + \\cos \\alpha_1 \\sin \\alpha_2 \\\\\n", "\\cos(\\alpha_1 + \\alpha_2) = \\cos \\alpha_1 \\cos \\alpha_2 - \\sin \\alpha_1 \\sin \\alpha_2$$\n", "\n", "Replacing $(x, y)$ with $(\\sin \\alpha, \\cos \\alpha)$ we get\n", "$$(x_1,y_1),(x_2,y_2) \\mapsto (x_1y_2 + y_1x_2, y_1y_2 - x_1x_2)$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "x, y = polygen(QQ, 'x, y')\n", "unit_circle = Curve(y**2 + x**2 - 1)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def add_circle(P1, P2):\n", " x1, y1 = P1\n", " x2, y2 = P2\n", " return (x1 * y2 + y1 * x2, y1 * y2 - x1 * x2)\n", " " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "P1 = (3/5, 4/5)\n", "P2 = (5/13, 12/13)\n", "P3 = add_circle(P1, P2)\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P1 == add_circle(P1, (0, 1))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graphic = plot(unit_circle)\n", "graphic+= point(P1, size = 50, color = 'red', legend_label = 'P1') \n", "graphic+= point(P2, size = 50, color = 'green', legend_label = 'P2')\n", "graphic+=point(P3, size = 50, color = 'cyan', legend_label = 'P3')\n", "\n", "plot(graphic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Edwards curves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Definition 1** --Original proposed form \n", "$$x^2 + y^2 = c^2 + c^2x^2y^2$$\n", "- Over finite fields there are a few curves that can be expressed in this way. Therefore a new form was studied\n", "\n", "
\n", "\n", "**Definition 2** -- Bernstein and Lange simplified form \n", "An Edwards curve is defined over a field $K$ with $char(K) \\neq 2$ and $d \\in K \\setminus \\{0, 1\\}$\n", "\n", "$$x^2 + y^2 = c^2(1 + dx^2y^2)$$\n", "\n", "but all curves of this form are isomorphic to an easier form:\n", "\n", "$$\\boxed{x^2 + y^2 = 1 + dx^2y^2}$$\n", "- where $x^2 \\equiv d \\bmod p$ has no solution ($d$ is a nonsquare. Otherwise the addition law defined below will not be complete -- will not work for all pairs of inputs)\n", "\n", "\n", "We will use the simplified form" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/zademn/.conda/envs/crypto310/lib/python3.10/site-packages/sage/plot/contour_plot.py:988: UserWarning: pathological contour plot of a function whose values all lie on one side of the sole contour; we are adding more plot points and perturbing your function values.\n", " warn(\"pathological contour plot of a function whose \"\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Play with the original form\n", "\n", "x, y = polygen(QQ, 'x, y')\n", "unit_circle = Curve(y**2 + x**2 - 1)\n", "\n", "c1, c2, c3 = 0, 2, 5# play with these\n", "ed1 = Curve(y**2 + x**2 - c1**2 - c1**2 * x**2 * y**2)\n", "ed2 = Curve(y**2 + x**2 - c2**2 - c2**2 * x**2 * y**2)\n", "ed3 = Curve(y**2 + x**2 - c3**2 - c3**2 * x**2 * y**2)\n", "\n", "graphic = ed1.plot() + ed2.plot(color = 'red') + ed3.plot(color = 'green')\n", "plot(graphic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The group structure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Addition** \n", "$$(x_{1},y_{1})+(x_{2},y_{2})=\\left({\\frac {x_{1}y_{2}+x_{2}y_{1}}{1+dx_{1}x_{2}y_{1}y_{2}}},{\\frac {y_{1}y_{2}-x_{1}x_{2}}{1-dx_{1}x_{2}y_{1}y_{2}}}\\right)$$\n", "\n", "**Identity**: $(0, 1)$\n", "\n", "**Negation**: $(x, y) \\mapsto (-x, y)$\n", "\n", "**Note**\n", "- Doubling can be performed with the same formula as addition\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def add_edwards(P1, P2):\n", " x1, y1 = P1\n", " x2, y2 = P2\n", " x3 = (x1 * y2 + y1 * x2) / (1 + d * x1 * x2 * y1 * y2)\n", " y3 = (y1 * y2 - x1 * x2) / (1 - d * x1 * x2 * y1 * y2)\n", " return (x3 , y3)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "x, y = polygen(GF(19), 'x, y')\n", "d = -30\n", "ed = Curve(y**2 + x**2 - 1 - d * x**2 * y**2)\n", "\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "P1 = ed.point_set().points()[15]\n", "P2 = ed.point_set().points()[12]\n", "P3 = add_edwards(P1, P2)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(3, 14)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P3" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graphic = point(ed.point_set().points())\n", "graphic+= point([P1], size = 50, color = 'red', legend_label = f'P1 = {P1}') \n", "graphic+= point([P2], size = 50, color = 'green', legend_label = f'P2 = {P2}')\n", "graphic+=point([P3], size = 50, color = 'cyan', legend_label = f'P3 = {P3}')\n", "\n", "plot(graphic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Special points" ] }, { "attachments": { "0d5b76e6-6d46-447e-b82c-2de1e686646d.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "The edwards curve equation is symmetric => $(x, y)$ can be interchanged. Therefore if $(x, y)$ is a solution $\\Rightarrow (\\pm x, \\pm y)$ and $(\\pm y, \\pm x)$ are solutions as well\n", "\n", "Four easy solutions: $\\{(0, 1), (0, -1), (1, 0), (-1, 0)\\}$.\n", "\n", "Using this solutions you can build rotations and reflections of points\n", "\n", "![image.png](attachment:0d5b76e6-6d46-447e-b82c-2de1e686646d.png)\n", "\n", "These 4 solutions form a cyclic group of order 4 with the generator $(-1, 0)$ or $(1, 0)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Connection with elliptic curves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Every Edwards curve is birationally equivalent to an elliptic curve over the same field. But in its construction we must assure that the curve has a point of order 4\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**From Edwards to an elliptic curve**\n", "Let $e = 1 - d$. Then we construct the curve\n", "$$\\dfrac 1 e v^2 = u^3 + \\left(\\dfrac 4 e - 2 \\right)u^2 + u$$\n", "\n", "With the following transformation\n", "$$(x, y) \\mapsto (u, v) = \\left( \\dfrac {1 + y} {1 - y} , \\dfrac {2(1 + y)} {x(1-y)} \\right) \\\\ (0, 1) \\mapsto \\mathcal{O}$$\n", "\n", "**Reverse map to Edwards**\n", "$$(u, v) \\mapsto (x, y) = \\left( \\dfrac {2u} v, \\dfrac {u-1} {u+1} \\right)$$" ] }, { "attachments": { "d20dc8b0-d1f5-4602-b7a9-6b32227bf6d9.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Direct maps to Weierstrass curves:** \n", "- https://fse.studenttheses.ub.rug.nl/10478/1/Marion_Dam_2012_WB_1.pdf -- Chapter 4 -- page 15 or from conclusion on page 29\n", "\n", "![image.png](attachment:d20dc8b0-d1f5-4602-b7a9-6b32227bf6d9.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Twisted Edwards curves\n", "- https://eprint.iacr.org/2008/013.pdf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Motivation**\n", "- These curves represent a generalisation of Edwards curves\n", "- The existence of points of order 4 restricts the number of elliptic curves in Edwards form over a field $K$.\n", "\n", "**Definition** \n", "A twisted Edwards curve is defined over a field $K$ with $char(K) \\neq 2$\n", "$$\\boxed{ax^2 + y^2 = 1 + dx^2y^2} \\ a \\neq d \\neq 0$$\n", "- $a = 1$ is the simple Edward curve\n", "\n", "\n", "**j-invariant**\n", "$$\\dfrac {16(a^2 + 14ad + d^2)^3} {ad(a -d)^4}$$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Play with the simplified form\n", "\n", "x, y = polygen(QQ, 'x, y')\n", "unit_circle = Curve(y**2 + x**2 - 1)\n", "\n", "a1, a2, a3 = 1, 2, 10\n", "d1, d2, d3 = 6, -10, -100 # play with these\n", "ed1 = Curve(y**2 + a1 * x**2 - 1 - d1 * x**2 * y**2)\n", "ed2 = Curve(y**2 + a2 * x**2 - 1 - d2 * x**2 * y**2)\n", "ed3 = Curve(y**2 + a3 * x**2 - 1 - d3 * x**2 * y**2)\n", "\n", "graphic = plot(ed1) + plot(ed2, color = 'red') + plot(ed3, color = 'green')\n", "graphic.set_axes_range(xmin = -3, xmax = 3, ymin = -3, ymax = 3)\n", "\n", "plot(graphic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The group structure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Addition** \n", "$$(x_{1},y_{1})+(x_{2},y_{2})=\\left({\\frac {x_{1}y_{2}+x_{2}y_{1}}{1+dx_{1}x_{2}y_{1}y_{2}}},{\\frac {y_{1}y_{2}-ax_{1}x_{2}}{1-dx_{1}x_{2}y_{1}y_{2}}}\\right)$$\n", "\n", "**Identity**: $(0, 1)$\n", "\n", "**Negation**: $(x, y) \\mapsto (-x, y)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Twisted Edwards and Montgomery curves" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Every twisted Edwards curve is birationally equivalent to an elliptic curve in Montgomery form and vice versa." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Montgomery curve: $M_{A,B}:By^{2}=x^{3}+Ax^{2}+x$\n", "\n", "**From Twisted Edwards to Montgomery**\n", "\n", "$$(x, y) \\mapsto (u, v) = \\left(\\dfrac {1 + y} {1 - y}, \\ \\dfrac {1 + y} {x(1 - y)} \\right);\n", "\\quad A = \\dfrac {2(a + d)} {a - d}, \\ B = \\dfrac 4 {a - d}$$\n", "\n", "**From Montgomery to Twisted edwards** \n", "\n", "$$(u, v) \\mapsto (x, y) = \\left( \\dfrac u v, \\dfrac {(u - 1)} {(u + 1)} \\right) \\quad a = \\dfrac {A + 2} B ,\\ d = \\dfrac {A - 2} B$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Resources\n", "- [Original paper](https://cr.yp.to/newelliptic/S0273-0979-07-01153-6.pdf)\n", "- [Edwards curves wikipedia](https://en.wikipedia.org/wiki/Edwards_curve)\n", "- [Twisted Edwards curves wikipedia](https://en.wikipedia.org/wiki/Twisted_Edwards_curve)\n", "- [Bernstein and Lange paper](https://cr.yp.to/newelliptic/newelliptic-20070906.pdf)\n", "- https://christianepeters.files.wordpress.com/2012/10/20110510-diss.pdf\n", "- https://fse.studenttheses.ub.rug.nl/10478/1/Marion_Dam_2012_WB_1.pdf" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.4" } }, "nbformat": 4, "nbformat_minor": 4 }