How to use red method in green

Best Python code snippet using green

short.js

Source:short.js Github

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1/​* */​ 2'use strict';3var curve = require('./​index');4var elliptic = require('../​../​elliptic');5var BN = require('bn.js');6var inherits = require('inherits');7var Base = curve.base;8var assert = elliptic.utils.assert;9function ShortCurve(conf) {10 Base.call(this, 'short', conf);11 this.a = new BN(conf.a, 16).toRed(this.red);12 this.b = new BN(conf.b, 16).toRed(this.red);13 this.tinv = this.two.redInvm();14 this.zeroA = this.a.fromRed().cmpn(0) === 0;15 this.threeA = this.a.fromRed().sub(this.p).cmpn(-3) === 0;16 this.endo = this._getEndomorphism(conf);17 this._endoWnafT1 = new Array(4);18 this._endoWnafT2 = new Array(4);19}20inherits(ShortCurve, Base);21module.exports = ShortCurve;22ShortCurve.prototype._getEndomorphism = function _getEndomorphism(conf) {23 if (!this.zeroA || !this.g || !this.n || this.p.modn(3) !== 1)24 return;25 var beta;26 var lambda;27 if (conf.beta) {28 beta = new BN(conf.beta, 16).toRed(this.red);29 } else {30 var betas = this._getEndoRoots(this.p);31 beta = betas[0].cmp(betas[1]) < 0 ? betas[0] : betas[1];32 beta = beta.toRed(this.red);33 }34 if (conf.lambda) {35 lambda = new BN(conf.lambda, 16);36 } else {37 var lambdas = this._getEndoRoots(this.n);38 if (this.g.mul(lambdas[0]).x.cmp(this.g.x.redMul(beta)) === 0) {39 lambda = lambdas[0];40 } else {41 lambda = lambdas[1];42 assert(this.g.mul(lambda).x.cmp(this.g.x.redMul(beta)) === 0);43 }44 }45 var basis;46 if (conf.basis) {47 basis = conf.basis.map(function(vec) {48 return {49 a: new BN(vec.a, 16),50 b: new BN(vec.b, 16)51 };52 });53 } else {54 basis = this._getEndoBasis(lambda);55 }56 return {57 beta: beta,58 lambda: lambda,59 basis: basis60 };61};62ShortCurve.prototype._getEndoRoots = function _getEndoRoots(num) {63 var red = num === this.p ? this.red : BN.mont(num);64 var tinv = new BN(2).toRed(red).redInvm();65 var ntinv = tinv.redNeg();66 var s = new BN(3).toRed(red).redNeg().redSqrt().redMul(tinv);67 var l1 = ntinv.redAdd(s).fromRed();68 var l2 = ntinv.redSub(s).fromRed();69 return [l1, l2];70};71ShortCurve.prototype._getEndoBasis = function _getEndoBasis(lambda) {72 var aprxSqrt = this.n.ushrn(Math.floor(this.n.bitLength() /​ 2));73 var u = lambda;74 var v = this.n.clone();75 var x1 = new BN(1);76 var y1 = new BN(0);77 var x2 = new BN(0);78 var y2 = new BN(1);79 var a0;80 var b0;81 var a1;82 var b1;83 var a2;84 var b2;85 var prevR;86 var i = 0;87 var r;88 var x;89 while (u.cmpn(0) !== 0) {90 var q = v.div(u);91 r = v.sub(q.mul(u));92 x = x2.sub(q.mul(x1));93 var y = y2.sub(q.mul(y1));94 if (!a1 && r.cmp(aprxSqrt) < 0) {95 a0 = prevR.neg();96 b0 = x1;97 a1 = r.neg();98 b1 = x;99 } else if (a1 && ++i === 2) {100 break;101 }102 prevR = r;103 v = u;104 u = r;105 x2 = x1;106 x1 = x;107 y2 = y1;108 y1 = y;109 }110 a2 = r.neg();111 b2 = x;112 var len1 = a1.sqr().add(b1.sqr());113 var len2 = a2.sqr().add(b2.sqr());114 if (len2.cmp(len1) >= 0) {115 a2 = a0;116 b2 = b0;117 }118 if (a1.negative) {119 a1 = a1.neg();120 b1 = b1.neg();121 }122 if (a2.negative) {123 a2 = a2.neg();124 b2 = b2.neg();125 }126 return [{127 a: a1,128 b: b1129 }, {130 a: a2,131 b: b2132 }];133};134ShortCurve.prototype._endoSplit = function _endoSplit(k) {135 var basis = this.endo.basis;136 var v1 = basis[0];137 var v2 = basis[1];138 var c1 = v2.b.mul(k).divRound(this.n);139 var c2 = v1.b.neg().mul(k).divRound(this.n);140 var p1 = c1.mul(v1.a);141 var p2 = c2.mul(v2.a);142 var q1 = c1.mul(v1.b);143 var q2 = c2.mul(v2.b);144 var k1 = k.sub(p1).sub(p2);145 var k2 = q1.add(q2).neg();146 return {147 k1: k1,148 k2: k2149 };150};151ShortCurve.prototype.pointFromX = function pointFromX(x, odd) {152 x = new BN(x, 16);153 if (!x.red)154 x = x.toRed(this.red);155 var y2 = x.redSqr().redMul(x).redIAdd(x.redMul(this.a)).redIAdd(this.b);156 var y = y2.redSqrt();157 if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)158 throw new Error('invalid point');159 var isOdd = y.fromRed().isOdd();160 if (odd && !isOdd || !odd && isOdd)161 y = y.redNeg();162 return this.point(x, y);163};164ShortCurve.prototype.validate = function validate(point) {165 if (point.inf)166 return true;167 var x = point.x;168 var y = point.y;169 var ax = this.a.redMul(x);170 var rhs = x.redSqr().redMul(x).redIAdd(ax).redIAdd(this.b);171 return y.redSqr().redISub(rhs).cmpn(0) === 0;172};173ShortCurve.prototype._endoWnafMulAdd = function _endoWnafMulAdd(points, coeffs) {174 var npoints = this._endoWnafT1;175 var ncoeffs = this._endoWnafT2;176 for (var i = 0; i < points.length; i++) {177 var split = this._endoSplit(coeffs[i]);178 var p = points[i];179 var beta = p._getBeta();180 if (split.k1.negative) {181 split.k1.ineg();182 p = p.neg(true);183 }184 if (split.k2.negative) {185 split.k2.ineg();186 beta = beta.neg(true);187 }188 npoints[i * 2] = p;189 npoints[i * 2 + 1] = beta;190 ncoeffs[i * 2] = split.k1;191 ncoeffs[i * 2 + 1] = split.k2;192 }193 var res = this._wnafMulAdd(1, npoints, ncoeffs, i * 2);194 for (var j = 0; j < i * 2; j++) {195 npoints[j] = null;196 ncoeffs[j] = null;197 }198 return res;199};200function Point(curve, x, y, isRed) {201 Base.BasePoint.call(this, curve, 'affine');202 if (x === null && y === null) {203 this.x = null;204 this.y = null;205 this.inf = true;206 } else {207 this.x = new BN(x, 16);208 this.y = new BN(y, 16);209 if (isRed) {210 this.x.forceRed(this.curve.red);211 this.y.forceRed(this.curve.red);212 }213 if (!this.x.red)214 this.x = this.x.toRed(this.curve.red);215 if (!this.y.red)216 this.y = this.y.toRed(this.curve.red);217 this.inf = false;218 }219}220inherits(Point, Base.BasePoint);221ShortCurve.prototype.point = function point(x, y, isRed) {222 return new Point(this, x, y, isRed);223};224ShortCurve.prototype.pointFromJSON = function pointFromJSON(obj, red) {225 return Point.fromJSON(this, obj, red);226};227Point.prototype._getBeta = function _getBeta() {228 if (!this.curve.endo)229 return;230 var pre = this.precomputed;231 if (pre && pre.beta)232 return pre.beta;233 var beta = this.curve.point(this.x.redMul(this.curve.endo.beta), this.y);234 if (pre) {235 var curve = this.curve;236 var endoMul = function(p) {237 return curve.point(p.x.redMul(curve.endo.beta), p.y);238 };239 pre.beta = beta;240 beta.precomputed = {241 beta: null,242 naf: pre.naf && {243 wnd: pre.naf.wnd,244 points: pre.naf.points.map(endoMul)245 },246 doubles: pre.doubles && {247 step: pre.doubles.step,248 points: pre.doubles.points.map(endoMul)249 }250 };251 }252 return beta;253};254Point.prototype.toJSON = function toJSON() {255 if (!this.precomputed)256 return [this.x, this.y];257 return [this.x, this.y, this.precomputed && {258 doubles: this.precomputed.doubles && {259 step: this.precomputed.doubles.step,260 points: this.precomputed.doubles.points.slice(1)261 },262 naf: this.precomputed.naf && {263 wnd: this.precomputed.naf.wnd,264 points: this.precomputed.naf.points.slice(1)265 }266 }];267};268Point.fromJSON = function fromJSON(curve, obj, red) {269 if (typeof obj === 'string')270 obj = JSON.parse(obj);271 var res = curve.point(obj[0], obj[1], red);272 if (!obj[2])273 return res;274 function obj2point(obj) {275 return curve.point(obj[0], obj[1], red);276 }277 var pre = obj[2];278 res.precomputed = {279 beta: null,280 doubles: pre.doubles && {281 step: pre.doubles.step,282 points: [res].concat(pre.doubles.points.map(obj2point))283 },284 naf: pre.naf && {285 wnd: pre.naf.wnd,286 points: [res].concat(pre.naf.points.map(obj2point))287 }288 };289 return res;290};291Point.prototype.inspect = function inspect() {292 if (this.isInfinity())293 return '<EC Point Infinity>';294 return '<EC Point x: ' + this.x.fromRed().toString(16, 2) + ' y: ' + this.y.fromRed().toString(16, 2) + '>';295};296Point.prototype.isInfinity = function isInfinity() {297 return this.inf;298};299Point.prototype.add = function add(p) {300 if (this.inf)301 return p;302 if (p.inf)303 return this;304 if (this.eq(p))305 return this.dbl();306 if (this.neg().eq(p))307 return this.curve.point(null, null);308 if (this.x.cmp(p.x) === 0)309 return this.curve.point(null, null);310 var c = this.y.redSub(p.y);311 if (c.cmpn(0) !== 0)312 c = c.redMul(this.x.redSub(p.x).redInvm());313 var nx = c.redSqr().redISub(this.x).redISub(p.x);314 var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);315 return this.curve.point(nx, ny);316};317Point.prototype.dbl = function dbl() {318 if (this.inf)319 return this;320 var ys1 = this.y.redAdd(this.y);321 if (ys1.cmpn(0) === 0)322 return this.curve.point(null, null);323 var a = this.curve.a;324 var x2 = this.x.redSqr();325 var dyinv = ys1.redInvm();326 var c = x2.redAdd(x2).redIAdd(x2).redIAdd(a).redMul(dyinv);327 var nx = c.redSqr().redISub(this.x.redAdd(this.x));328 var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);329 return this.curve.point(nx, ny);330};331Point.prototype.getX = function getX() {332 return this.x.fromRed();333};334Point.prototype.getY = function getY() {335 return this.y.fromRed();336};337Point.prototype.mul = function mul(k) {338 k = new BN(k, 16);339 if (this._hasDoubles(k))340 return this.curve._fixedNafMul(this, k);341 else if (this.curve.endo)342 return this.curve._endoWnafMulAdd([this], [k]);343 else344 return this.curve._wnafMul(this, k);345};346Point.prototype.mulAdd = function mulAdd(k1, p2, k2) {347 var points = [this, p2];348 var coeffs = [k1, k2];349 if (this.curve.endo)350 return this.curve._endoWnafMulAdd(points, coeffs);351 else352 return this.curve._wnafMulAdd(1, points, coeffs, 2);353};354Point.prototype.eq = function eq(p) {355 return this === p || this.inf === p.inf && (this.inf || this.x.cmp(p.x) === 0 && this.y.cmp(p.y) === 0);356};357Point.prototype.neg = function neg(_precompute) {358 if (this.inf)359 return this;360 var res = this.curve.point(this.x, this.y.redNeg());361 if (_precompute && this.precomputed) {362 var pre = this.precomputed;363 var negate = function(p) {364 return p.neg();365 };366 res.precomputed = {367 naf: pre.naf && {368 wnd: pre.naf.wnd,369 points: pre.naf.points.map(negate)370 },371 doubles: pre.doubles && {372 step: pre.doubles.step,373 points: pre.doubles.points.map(negate)374 }375 };376 }377 return res;378};379Point.prototype.toJ = function toJ() {380 if (this.inf)381 return this.curve.jpoint(null, null, null);382 var res = this.curve.jpoint(this.x, this.y, this.curve.one);383 return res;384};385function JPoint(curve, x, y, z) {386 Base.BasePoint.call(this, curve, 'jacobian');387 if (x === null && y === null && z === null) {388 this.x = this.curve.one;389 this.y = this.curve.one;390 this.z = new BN(0);391 } else {392 this.x = new BN(x, 16);393 this.y = new BN(y, 16);394 this.z = new BN(z, 16);395 }396 if (!this.x.red)397 this.x = this.x.toRed(this.curve.red);398 if (!this.y.red)399 this.y = this.y.toRed(this.curve.red);400 if (!this.z.red)401 this.z = this.z.toRed(this.curve.red);402 this.zOne = this.z === this.curve.one;403}404inherits(JPoint, Base.BasePoint);405ShortCurve.prototype.jpoint = function jpoint(x, y, z) {406 return new JPoint(this, x, y, z);407};408JPoint.prototype.toP = function toP() {409 if (this.isInfinity())410 return this.curve.point(null, null);411 var zinv = this.z.redInvm();412 var zinv2 = zinv.redSqr();413 var ax = this.x.redMul(zinv2);414 var ay = this.y.redMul(zinv2).redMul(zinv);415 return this.curve.point(ax, ay);416};417JPoint.prototype.neg = function neg() {418 return this.curve.jpoint(this.x, this.y.redNeg(), this.z);419};420JPoint.prototype.add = function add(p) {421 if (this.isInfinity())422 return p;423 if (p.isInfinity())424 return this;425 var pz2 = p.z.redSqr();426 var z2 = this.z.redSqr();427 var u1 = this.x.redMul(pz2);428 var u2 = p.x.redMul(z2);429 var s1 = this.y.redMul(pz2.redMul(p.z));430 var s2 = p.y.redMul(z2.redMul(this.z));431 var h = u1.redSub(u2);432 var r = s1.redSub(s2);433 if (h.cmpn(0) === 0) {434 if (r.cmpn(0) !== 0)435 return this.curve.jpoint(null, null, null);436 else437 return this.dbl();438 }439 var h2 = h.redSqr();440 var h3 = h2.redMul(h);441 var v = u1.redMul(h2);442 var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);443 var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));444 var nz = this.z.redMul(p.z).redMul(h);445 return this.curve.jpoint(nx, ny, nz);446};447JPoint.prototype.mixedAdd = function mixedAdd(p) {448 if (this.isInfinity())449 return p.toJ();450 if (p.isInfinity())451 return this;452 var z2 = this.z.redSqr();453 var u1 = this.x;454 var u2 = p.x.redMul(z2);455 var s1 = this.y;456 var s2 = p.y.redMul(z2).redMul(this.z);457 var h = u1.redSub(u2);458 var r = s1.redSub(s2);459 if (h.cmpn(0) === 0) {460 if (r.cmpn(0) !== 0)461 return this.curve.jpoint(null, null, null);462 else463 return this.dbl();464 }465 var h2 = h.redSqr();466 var h3 = h2.redMul(h);467 var v = u1.redMul(h2);468 var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);469 var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));470 var nz = this.z.redMul(h);471 return this.curve.jpoint(nx, ny, nz);472};473JPoint.prototype.dblp = function dblp(pow) {474 if (pow === 0)475 return this;476 if (this.isInfinity())477 return this;478 if (!pow)479 return this.dbl();480 if (this.curve.zeroA || this.curve.threeA) {481 var r = this;482 for (var i = 0; i < pow; i++)483 r = r.dbl();484 return r;485 }486 var a = this.curve.a;487 var tinv = this.curve.tinv;488 var jx = this.x;489 var jy = this.y;490 var jz = this.z;491 var jz4 = jz.redSqr().redSqr();492 var jyd = jy.redAdd(jy);493 for (var i = 0; i < pow; i++) {494 var jx2 = jx.redSqr();495 var jyd2 = jyd.redSqr();496 var jyd4 = jyd2.redSqr();497 var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));498 var t1 = jx.redMul(jyd2);499 var nx = c.redSqr().redISub(t1.redAdd(t1));500 var t2 = t1.redISub(nx);501 var dny = c.redMul(t2);502 dny = dny.redIAdd(dny).redISub(jyd4);503 var nz = jyd.redMul(jz);504 if (i + 1 < pow)505 jz4 = jz4.redMul(jyd4);506 jx = nx;507 jz = nz;508 jyd = dny;509 }510 return this.curve.jpoint(jx, jyd.redMul(tinv), jz);511};512JPoint.prototype.dbl = function dbl() {513 if (this.isInfinity())514 return this;515 if (this.curve.zeroA)516 return this._zeroDbl();517 else if (this.curve.threeA)518 return this._threeDbl();519 else520 return this._dbl();521};522JPoint.prototype._zeroDbl = function _zeroDbl() {523 var nx;524 var ny;525 var nz;526 if (this.zOne) {527 var xx = this.x.redSqr();528 var yy = this.y.redSqr();529 var yyyy = yy.redSqr();530 var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);531 s = s.redIAdd(s);532 var m = xx.redAdd(xx).redIAdd(xx);533 var t = m.redSqr().redISub(s).redISub(s);534 var yyyy8 = yyyy.redIAdd(yyyy);535 yyyy8 = yyyy8.redIAdd(yyyy8);536 yyyy8 = yyyy8.redIAdd(yyyy8);537 nx = t;538 ny = m.redMul(s.redISub(t)).redISub(yyyy8);539 nz = this.y.redAdd(this.y);540 } else {541 var a = this.x.redSqr();542 var b = this.y.redSqr();543 var c = b.redSqr();544 var d = this.x.redAdd(b).redSqr().redISub(a).redISub(c);545 d = d.redIAdd(d);546 var e = a.redAdd(a).redIAdd(a);547 var f = e.redSqr();548 var c8 = c.redIAdd(c);549 c8 = c8.redIAdd(c8);550 c8 = c8.redIAdd(c8);551 nx = f.redISub(d).redISub(d);552 ny = e.redMul(d.redISub(nx)).redISub(c8);553 nz = this.y.redMul(this.z);554 nz = nz.redIAdd(nz);555 }556 return this.curve.jpoint(nx, ny, nz);557};558JPoint.prototype._threeDbl = function _threeDbl() {559 var nx;560 var ny;561 var nz;562 if (this.zOne) {563 var xx = this.x.redSqr();564 var yy = this.y.redSqr();565 var yyyy = yy.redSqr();566 var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);567 s = s.redIAdd(s);568 var m = xx.redAdd(xx).redIAdd(xx).redIAdd(this.curve.a);569 var t = m.redSqr().redISub(s).redISub(s);570 nx = t;571 var yyyy8 = yyyy.redIAdd(yyyy);572 yyyy8 = yyyy8.redIAdd(yyyy8);573 yyyy8 = yyyy8.redIAdd(yyyy8);574 ny = m.redMul(s.redISub(t)).redISub(yyyy8);575 nz = this.y.redAdd(this.y);576 } else {577 var delta = this.z.redSqr();578 var gamma = this.y.redSqr();579 var beta = this.x.redMul(gamma);580 var alpha = this.x.redSub(delta).redMul(this.x.redAdd(delta));581 alpha = alpha.redAdd(alpha).redIAdd(alpha);582 var beta4 = beta.redIAdd(beta);583 beta4 = beta4.redIAdd(beta4);584 var beta8 = beta4.redAdd(beta4);585 nx = alpha.redSqr().redISub(beta8);586 nz = this.y.redAdd(this.z).redSqr().redISub(gamma).redISub(delta);587 var ggamma8 = gamma.redSqr();588 ggamma8 = ggamma8.redIAdd(ggamma8);589 ggamma8 = ggamma8.redIAdd(ggamma8);590 ggamma8 = ggamma8.redIAdd(ggamma8);591 ny = alpha.redMul(beta4.redISub(nx)).redISub(ggamma8);592 }593 return this.curve.jpoint(nx, ny, nz);594};595JPoint.prototype._dbl = function _dbl() {596 var a = this.curve.a;597 var jx = this.x;598 var jy = this.y;599 var jz = this.z;600 var jz4 = jz.redSqr().redSqr();601 var jx2 = jx.redSqr();602 var jy2 = jy.redSqr();603 var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));604 var jxd4 = jx.redAdd(jx);605 jxd4 = jxd4.redIAdd(jxd4);606 var t1 = jxd4.redMul(jy2);607 var nx = c.redSqr().redISub(t1.redAdd(t1));608 var t2 = t1.redISub(nx);609 var jyd8 = jy2.redSqr();610 jyd8 = jyd8.redIAdd(jyd8);611 jyd8 = jyd8.redIAdd(jyd8);612 jyd8 = jyd8.redIAdd(jyd8);613 var ny = c.redMul(t2).redISub(jyd8);614 var nz = jy.redAdd(jy).redMul(jz);615 return this.curve.jpoint(nx, ny, nz);616};617JPoint.prototype.trpl = function trpl() {618 if (!this.curve.zeroA)619 return this.dbl().add(this);620 var xx = this.x.redSqr();621 var yy = this.y.redSqr();622 var zz = this.z.redSqr();623 var yyyy = yy.redSqr();624 var m = xx.redAdd(xx).redIAdd(xx);625 var mm = m.redSqr();626 var e = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);627 e = e.redIAdd(e);628 e = e.redAdd(e).redIAdd(e);629 e = e.redISub(mm);630 var ee = e.redSqr();631 var t = yyyy.redIAdd(yyyy);632 t = t.redIAdd(t);633 t = t.redIAdd(t);634 t = t.redIAdd(t);635 var u = m.redIAdd(e).redSqr().redISub(mm).redISub(ee).redISub(t);636 var yyu4 = yy.redMul(u);637 yyu4 = yyu4.redIAdd(yyu4);638 yyu4 = yyu4.redIAdd(yyu4);639 var nx = this.x.redMul(ee).redISub(yyu4);640 nx = nx.redIAdd(nx);641 nx = nx.redIAdd(nx);642 var ny = this.y.redMul(u.redMul(t.redISub(u)).redISub(e.redMul(ee)));643 ny = ny.redIAdd(ny);644 ny = ny.redIAdd(ny);645 ny = ny.redIAdd(ny);646 var nz = this.z.redAdd(e).redSqr().redISub(zz).redISub(ee);647 return this.curve.jpoint(nx, ny, nz);648};649JPoint.prototype.mul = function mul(k, kbase) {650 k = new BN(k, kbase);651 return this.curve._wnafMul(this, k);652};653JPoint.prototype.eq = function eq(p) {654 if (p.type === 'affine')655 return this.eq(p.toJ());656 if (this === p)657 return true;658 var z2 = this.z.redSqr();659 var pz2 = p.z.redSqr();660 if (this.x.redMul(pz2).redISub(p.x.redMul(z2)).cmpn(0) !== 0)661 return false;662 var z3 = z2.redMul(this.z);663 var pz3 = pz2.redMul(p.z);664 return this.y.redMul(pz3).redISub(p.y.redMul(z3)).cmpn(0) === 0;665};666JPoint.prototype.inspect = function inspect() {667 if (this.isInfinity())668 return '<EC JPoint Infinity>';669 return '<EC JPoint x: ' + this.x.toString(16, 2) + ' y: ' + this.y.toString(16, 2) + ' z: ' + this.z.toString(16, 2) + '>';670};671JPoint.prototype.isInfinity = function isInfinity() {672 return this.z.cmpn(0) === 0;...

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rbtree.py

Source:rbtree.py Github

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1class Node:2 def __init__(self, key):3 self.key = key4 self.red = True5 self.right = None6 self.left = None7 self.parent = None8class RBtree(Node):9 def __init__(self):10 self.root = None11 def insert(self, key):12 node = Node(key)13 node.red = True14 if self.root == None:15 node.red = False16 self.root = node17 node.left = Node(None)18 node.left.red = False19 node.right = Node(None)20 node.right.red = False21 return22 currentNode = self.root23 while currentNode.key != None:24 potentialParent = currentNode25 if node.key < currentNode.key:26 currentNode = currentNode.left27 else:28 currentNode = currentNode.right29 node.parent = potentialParent30 if node.key < node.parent.key:31 currentNode.left = node32 node.parent.left = node33 34 else:35 currentNode.right = node36 node.parent.right = node37 node.left = Node(None)38 node.left.red = False39 node.right = Node(None)40 node.right.red = False41 self._fixTree(node)42 def MinNode(self,key=None):43 if self.root is not None:44 current = self.root45 while (current.left.key is not None):46 current = current.left47 return current48 else:49 print("tree is empty")50 def MaxNode(self):51 if self.root is not None:52 current = self.root53 while (current.right.key is not None):54 current = current.right55 return current56 else:57 print("tree is empty")58 def search(self, key):59 if self.root is not None:60 currentNode = self.root61 while currentNode.key != None and key != currentNode.key:62 if key < currentNode.key:63 currentNode = currentNode.left64 else:65 currentNode = currentNode.right66 return currentNode67 else:68 print("tree is empty")69 def FindNext(self, x):70 current = self.search(x)71 if current:72 current = current.right73 if current.key is not None:74 while (current.left.key is not None):75 current = current.left76 return current77 else:78 print('x is not exist in tree')79 def FindPrev(self, x):80 current = self.search(x)81 if current:82 current=current.left83 if current.key is not None:84 while (current.right.key is not None):85 current = current.right86 return current87 else:88 print('x is not exist in tree')89 def deleteNode(self, key):90 currentNode = self.search(key)91 if currentNode is not self.root:92 if currentNode.key is not None:93 if currentNode == currentNode.parent.left:94 self._delete_left_node(currentNode)95 96 else:97 self._delete_right_node(currentNode)98 else:99 print("Node is not exists")100 else:101 self._delete_root_node(currentNode)102 103#________________auxiliary_methods______________104 105 def _fixTree(self, node):106 while node.parent is not None and node.parent.red == True:107 if node.parent == node.parent.parent.left:108 uncle = node.parent.parent.right109 if uncle.red:110 node.parent.red = False111 uncle.red = False112 node.parent.parent.red = True113 node = node.parent.parent114 else:115 if node == node.parent.right:116 node = node.parent117 self._left_rotate(node)118 node.parent.red = False119 node.parent.parent.red = True120 self._right_rotate(node.parent.parent)121 else:122 uncle = node.parent.parent.left123 if uncle.red:124 node.parent.red = False125 uncle.red = False126 node.parent.parent.red = True127 node = node.parent.parent128 else:129 if node == node.parent.left:130 node = node.parent131 self._right_rotate(node)132 node.parent.red = False133 node.parent.parent.red = True134 self._left_rotate(node.parent.parent)135 self.root.red = False 136 137 def _left_rotate(self, node):138 sibling = node.right139 node.right = sibling.left140 if sibling.left != None:141 sibling.left.parent = node142 sibling.parent = node.parent143 if node.parent == None:144 self.root = sibling145 else:146 if node == node.parent.left:147 node.parent.left = sibling148 else:149 node.parent.right = sibling150 sibling.left = node151 node.parent = sibling152 def _right_rotate(self, node):153 sibling = node.left154 node.left = sibling.right155 if sibling.right != None:156 sibling.right.parent = node157 sibling.parent = node.parent158 if node.parent == None:159 self.root = sibling160 else:161 if node == node.parent.right:162 node.parent.right = sibling163 else:164 node.parent.left = sibling165 sibling.right = node166 node.parent = sibling167 168 169 170 def _delete_left_node(self,currentNode):171 if currentNode.left.key is None and currentNode.right.key is None:172 self._delete_left_node_noChildren(currentNode)173 elif currentNode.left.key is None and currentNode.right.key is not None:174 self._delete_left_node_onlyRightChildren(currentNode)175 elif currentNode.left.key is not None and currentNode.right.key is None:176 self._delete_left_node_onlyLeftChildren(currentNode)177 else:178 self._delete_left_node_bothChildren(currentNode)179 180 181 182 def _delete_right_node(self,currentNode):183 if currentNode.left.key is None and currentNode.right.key is None:184 self._delete_right_node_noChildren(currentNode) 185 186 elif currentNode.left.key is None and currentNode.right.key is not None:187 self._delete_right_node_onlyRightChildren(currentNode)188 elif currentNode.left.key is not None and currentNode.right.key is None:189 self._delete_right_node_onlyLeftChildren(currentNode)190 else:191 self._delete_right_node_bothChildren(currentNode)192 193 194 def _delete_root_node(self, currentNode):195 if currentNode.left.key is None and currentNode.right.key is None:196 self.root = None197 elif currentNode.left.key is None and currentNode.right.key is not None:198 self.root=currentNode.right199 currentNode.right.parent = None200 elif currentNode.left.key is not None and currentNode.right.key is None:201 self.root = currentNode.left202 currentNode.left.parent = None203 else:204 next = self.FindNext(currentNode.key)205 next.parent = None206 self.root = next207 currentNode.left.parent = self.root208 self.root.left = currentNode.left209 self.root.red = False210 211 def _delete_left_node_noChildren(self, currentNode):212 currentNode.parent.left = currentNode.left213 currentNode.left.parent = currentNode.parent214 if currentNode.red is False:215 brother = currentNode.parent.right216 if brother.red == False:217 if brother.left.red and brother.right.red:218 brother.right.red = False219 self._left_rotate(brother.parent)220 elif brother.left.red and brother.right.red==False:221 brother.left.red = False222 brother.red = True223 self._right_rotate(brother)224 self._left_rotate(brother.parent.parent)225 elif brother.right.red and brother.left.red == False:226 brother.right.red = False227 self._left_rotate(brother.parent) 228 else:229 if brother.left.key is not None and brother.right.key is not None:230 brother.red = False231 brother.left.red = True232 self._left_rotate(brother.parent)233 234 def _delete_left_node_onlyRightChildren(self, currentNode):235 currentNode.parent.left = currentNode.right236 currentNode.right.parent = currentNode.parent237 if currentNode.red is False:238 if currentNode.right.red:239 currentNode.right.red = False240 else:241 brother = currentNode.parent.right242 if brother.red == False:243 if brother.left.red and brother.right.red:244 brother.right.red = False245 self._left_rotate(brother.parent)246 elif brother.left.red and brother.right.red==False:247 brother.left.red = False248 brother.red = True249 self._right_rotate(brother)250 self._left_rotate(brother.parent.parent)251 elif brother.right.red and brother.left.red == False:252 brother.right.red = False253 self._left_rotate(brother.parent) 254 else:255 if brother.left.key is not None and brother.right.key is not None:256 brother.red = False257 brother.left.red = True258 self._left_rotate(brother.parent)259 260 def _delete_left_node_onlyLeftChildren(self, currentNode):261 currentNode.parent.left = currentNode.left262 currentNode.left.parent = currentNode.parent263 if currentNode.red is False:264 if currentNode.left.red:265 currentNode.left.red = False266 267 def _delete_left_node_bothChildren(self, currentNode):268 next = self.FindNext(currentNode.key)269 currentNode.parent.left = next270 next.parent = currentNode.parent271 currentNode.left.parent = next272 next.left = currentNode.left273 if next.red is False:274 if next.right.red:275 next.right.red = False276 next.red = True277 else:278 next.red = False279 def _delete_right_node_noChildren(self, currentNode):280 currentNode.parent.right = currentNode.right281 currentNode.right.parent = currentNode.parent282 if currentNode.red is False:283 brother = currentNode.parent.left284 print(brother.key)285 if brother.red == False:286 if brother.left.red and brother.right.red:287 brother.right.red = False288 self._right_rotate(brother.parent)289 elif brother.right.red and brother.left.red == False:290 brother.right.red = False291 brother.red = True292 self._left_rotate(brother)293 self._right_rotate(brother.parent.parent)294 elif brother.left.red and brother.right.red == False:295 brother.left.red = False296 self._right_rotate(brother.parent)297 298 else:299 if brother.left.key is not None and brother.right.key is not None:300 brother.red = False301 brother.right.red = True302 self._right_rotate(brother.parent)303 304 def _delete_right_node_onlyRightChildren(self, currentNode):305 currentNode.parent.right = currentNode.right306 currentNode.right.parent = currentNode.parent307 if currentNode.red is False:308 if currentNode.right.red:309 currentNode.right.red = False310 311 def _delete_right_node_onlyLeftChildren(self, currentNode):312 currentNode.parent.right = currentNode.left313 currentNode.left.parent = currentNode.parent314 if currentNode.red is False:315 if currentNode.left.red:316 currentNode.left.red = False317 318 def _delete_right_node_bothChildren(self, currentNode):319 next = self.FindNext(currentNode.key)320 currentNode.parent.right = next321 next.parent = currentNode.parent322 currentNode.left.parent= next323 next.left = currentNode.left324 print(next.key)325 326 if next.red is False:327 if next.right.red: 328 next.right.red = False329 next.red = True330 else:...

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edwards.js

Source:edwards.js Github

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1/​* */​ 2'use strict';3var curve = require('./​index');4var elliptic = require('../​../​elliptic');5var BN = require('bn.js');6var inherits = require('inherits');7var Base = curve.base;8var assert = elliptic.utils.assert;9function EdwardsCurve(conf) {10 this.twisted = (conf.a | 0) !== 1;11 this.mOneA = this.twisted && (conf.a | 0) === -1;12 this.extended = this.mOneA;13 Base.call(this, 'edwards', conf);14 this.a = new BN(conf.a, 16).umod(this.red.m);15 this.a = this.a.toRed(this.red);16 this.c = new BN(conf.c, 16).toRed(this.red);17 this.c2 = this.c.redSqr();18 this.d = new BN(conf.d, 16).toRed(this.red);19 this.dd = this.d.redAdd(this.d);20 assert(!this.twisted || this.c.fromRed().cmpn(1) === 0);21 this.oneC = (conf.c | 0) === 1;22}23inherits(EdwardsCurve, Base);24module.exports = EdwardsCurve;25EdwardsCurve.prototype._mulA = function _mulA(num) {26 if (this.mOneA)27 return num.redNeg();28 else29 return this.a.redMul(num);30};31EdwardsCurve.prototype._mulC = function _mulC(num) {32 if (this.oneC)33 return num;34 else35 return this.c.redMul(num);36};37EdwardsCurve.prototype.jpoint = function jpoint(x, y, z, t) {38 return this.point(x, y, z, t);39};40EdwardsCurve.prototype.pointFromX = function pointFromX(x, odd) {41 x = new BN(x, 16);42 if (!x.red)43 x = x.toRed(this.red);44 var x2 = x.redSqr();45 var rhs = this.c2.redSub(this.a.redMul(x2));46 var lhs = this.one.redSub(this.c2.redMul(this.d).redMul(x2));47 var y2 = rhs.redMul(lhs.redInvm());48 var y = y2.redSqrt();49 if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)50 throw new Error('invalid point');51 var isOdd = y.fromRed().isOdd();52 if (odd && !isOdd || !odd && isOdd)53 y = y.redNeg();54 return this.point(x, y);55};56EdwardsCurve.prototype.pointFromY = function pointFromY(y, odd) {57 y = new BN(y, 16);58 if (!y.red)59 y = y.toRed(this.red);60 var y2 = y.redSqr();61 var lhs = y2.redSub(this.one);62 var rhs = y2.redMul(this.d).redAdd(this.one);63 var x2 = lhs.redMul(rhs.redInvm());64 if (x2.cmp(this.zero) === 0) {65 if (odd)66 throw new Error('invalid point');67 else68 return this.point(this.zero, y);69 }70 var x = x2.redSqrt();71 if (x.redSqr().redSub(x2).cmp(this.zero) !== 0)72 throw new Error('invalid point');73 if (x.isOdd() !== odd)74 x = x.redNeg();75 return this.point(x, y);76};77EdwardsCurve.prototype.validate = function validate(point) {78 if (point.isInfinity())79 return true;80 point.normalize();81 var x2 = point.x.redSqr();82 var y2 = point.y.redSqr();83 var lhs = x2.redMul(this.a).redAdd(y2);84 var rhs = this.c2.redMul(this.one.redAdd(this.d.redMul(x2).redMul(y2)));85 return lhs.cmp(rhs) === 0;86};87function Point(curve, x, y, z, t) {88 Base.BasePoint.call(this, curve, 'projective');89 if (x === null && y === null && z === null) {90 this.x = this.curve.zero;91 this.y = this.curve.one;92 this.z = this.curve.one;93 this.t = this.curve.zero;94 this.zOne = true;95 } else {96 this.x = new BN(x, 16);97 this.y = new BN(y, 16);98 this.z = z ? new BN(z, 16) : this.curve.one;99 this.t = t && new BN(t, 16);100 if (!this.x.red)101 this.x = this.x.toRed(this.curve.red);102 if (!this.y.red)103 this.y = this.y.toRed(this.curve.red);104 if (!this.z.red)105 this.z = this.z.toRed(this.curve.red);106 if (this.t && !this.t.red)107 this.t = this.t.toRed(this.curve.red);108 this.zOne = this.z === this.curve.one;109 if (this.curve.extended && !this.t) {110 this.t = this.x.redMul(this.y);111 if (!this.zOne)112 this.t = this.t.redMul(this.z.redInvm());113 }114 }115}116inherits(Point, Base.BasePoint);117EdwardsCurve.prototype.pointFromJSON = function pointFromJSON(obj) {118 return Point.fromJSON(this, obj);119};120EdwardsCurve.prototype.point = function point(x, y, z, t) {121 return new Point(this, x, y, z, t);122};123Point.fromJSON = function fromJSON(curve, obj) {124 return new Point(curve, obj[0], obj[1], obj[2]);125};126Point.prototype.inspect = function inspect() {127 if (this.isInfinity())128 return '<EC Point Infinity>';129 return '<EC Point x: ' + this.x.fromRed().toString(16, 2) + ' y: ' + this.y.fromRed().toString(16, 2) + ' z: ' + this.z.fromRed().toString(16, 2) + '>';130};131Point.prototype.isInfinity = function isInfinity() {132 return this.x.cmpn(0) === 0 && this.y.cmp(this.z) === 0;133};134Point.prototype._extDbl = function _extDbl() {135 var a = this.x.redSqr();136 var b = this.y.redSqr();137 var c = this.z.redSqr();138 c = c.redIAdd(c);139 var d = this.curve._mulA(a);140 var e = this.x.redAdd(this.y).redSqr().redISub(a).redISub(b);141 var g = d.redAdd(b);142 var f = g.redSub(c);143 var h = d.redSub(b);144 var nx = e.redMul(f);145 var ny = g.redMul(h);146 var nt = e.redMul(h);147 var nz = f.redMul(g);148 return this.curve.point(nx, ny, nz, nt);149};150Point.prototype._projDbl = function _projDbl() {151 var b = this.x.redAdd(this.y).redSqr();152 var c = this.x.redSqr();153 var d = this.y.redSqr();154 var nx;155 var ny;156 var nz;157 if (this.curve.twisted) {158 var e = this.curve._mulA(c);159 var f = e.redAdd(d);160 if (this.zOne) {161 nx = b.redSub(c).redSub(d).redMul(f.redSub(this.curve.two));162 ny = f.redMul(e.redSub(d));163 nz = f.redSqr().redSub(f).redSub(f);164 } else {165 var h = this.z.redSqr();166 var j = f.redSub(h).redISub(h);167 nx = b.redSub(c).redISub(d).redMul(j);168 ny = f.redMul(e.redSub(d));169 nz = f.redMul(j);170 }171 } else {172 var e = c.redAdd(d);173 var h = this.curve._mulC(this.c.redMul(this.z)).redSqr();174 var j = e.redSub(h).redSub(h);175 nx = this.curve._mulC(b.redISub(e)).redMul(j);176 ny = this.curve._mulC(e).redMul(c.redISub(d));177 nz = e.redMul(j);178 }179 return this.curve.point(nx, ny, nz);180};181Point.prototype.dbl = function dbl() {182 if (this.isInfinity())183 return this;184 if (this.curve.extended)185 return this._extDbl();186 else187 return this._projDbl();188};189Point.prototype._extAdd = function _extAdd(p) {190 var a = this.y.redSub(this.x).redMul(p.y.redSub(p.x));191 var b = this.y.redAdd(this.x).redMul(p.y.redAdd(p.x));192 var c = this.t.redMul(this.curve.dd).redMul(p.t);193 var d = this.z.redMul(p.z.redAdd(p.z));194 var e = b.redSub(a);195 var f = d.redSub(c);196 var g = d.redAdd(c);197 var h = b.redAdd(a);198 var nx = e.redMul(f);199 var ny = g.redMul(h);200 var nt = e.redMul(h);201 var nz = f.redMul(g);202 return this.curve.point(nx, ny, nz, nt);203};204Point.prototype._projAdd = function _projAdd(p) {205 var a = this.z.redMul(p.z);206 var b = a.redSqr();207 var c = this.x.redMul(p.x);208 var d = this.y.redMul(p.y);209 var e = this.curve.d.redMul(c).redMul(d);210 var f = b.redSub(e);211 var g = b.redAdd(e);212 var tmp = this.x.redAdd(this.y).redMul(p.x.redAdd(p.y)).redISub(c).redISub(d);213 var nx = a.redMul(f).redMul(tmp);214 var ny;215 var nz;216 if (this.curve.twisted) {217 ny = a.redMul(g).redMul(d.redSub(this.curve._mulA(c)));218 nz = f.redMul(g);219 } else {220 ny = a.redMul(g).redMul(d.redSub(c));221 nz = this.curve._mulC(f).redMul(g);222 }223 return this.curve.point(nx, ny, nz);224};225Point.prototype.add = function add(p) {226 if (this.isInfinity())227 return p;228 if (p.isInfinity())229 return this;230 if (this.curve.extended)231 return this._extAdd(p);232 else233 return this._projAdd(p);234};235Point.prototype.mul = function mul(k) {236 if (this._hasDoubles(k))237 return this.curve._fixedNafMul(this, k);238 else239 return this.curve._wnafMul(this, k);240};241Point.prototype.mulAdd = function mulAdd(k1, p, k2) {242 return this.curve._wnafMulAdd(1, [this, p], [k1, k2], 2);243};244Point.prototype.normalize = function normalize() {245 if (this.zOne)246 return this;247 var zi = this.z.redInvm();248 this.x = this.x.redMul(zi);249 this.y = this.y.redMul(zi);250 if (this.t)251 this.t = this.t.redMul(zi);252 this.z = this.curve.one;253 this.zOne = true;254 return this;255};256Point.prototype.neg = function neg() {257 return this.curve.point(this.x.redNeg(), this.y, this.z, this.t && this.t.redNeg());258};259Point.prototype.getX = function getX() {260 this.normalize();261 return this.x.fromRed();262};263Point.prototype.getY = function getY() {264 this.normalize();265 return this.y.fromRed();266};267Point.prototype.eq = function eq(other) {268 return this === other || this.getX().cmp(other.getX()) === 0 && this.getY().cmp(other.getY()) === 0;269};270Point.prototype.toP = Point.prototype.normalize;...

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blur.py

Source:blur.py Github

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1"""2File: blur.py3Name:4-------------------------------5This file shows the original image first,6smiley-face.png, and then compare to its7blurred image. The blur algorithm uses the8average RGB values of a pixel's nearest neighbors.9"""10from simpleimage import SimpleImage11BLUR_INDEX = 512def main():13 """14 TODO: put in a picture and show the blurred version of it15 """16 old_img = SimpleImage("images/​smiley-face.png")17 old_img.show()18 blurred_img = blur(old_img)19 for i in range(BLUR_INDEX):20 blurred_img = blur(blurred_img)21 blurred_img.show()22def blur(img):23 """24 :param img: An image to be blurred25 :return: a blurred image26 """27 new_img = SimpleImage.blank(img.width, img.height)28 for x in range(img.width):29 for y in range(img.height):30 pixel = new_img.get_pixel(x, y)31 sum_red = 032 sum_blue = 033 sum_green = 034 if x == 0:35 if y == 0:36 for i in range(0, 2):37 for j in range(0, 2):38 neighbor = img.get_pixel(x + i, y + j)39 sum_red += neighbor.red40 sum_blue += neighbor.blue41 sum_green += neighbor.green42 pixel.red = sum_red /​ 443 pixel.blue = sum_blue /​ 444 pixel.green = sum_green /​ 445 elif y == img.height-1:46 for i in range(0, 2):47 for j in range(-1, 1):48 neighbor = img.get_pixel(x + i, y + j)49 sum_red += neighbor.red50 sum_blue += neighbor.blue51 sum_green += neighbor.green52 pixel.red = sum_red /​ 453 pixel.blue = sum_blue /​ 454 pixel.green = sum_green /​ 455 else:56 for i in range(0, 2):57 for j in range(-1, 2):58 neighbor = img.get_pixel(x + i, y + j)59 sum_red += neighbor.red60 sum_blue += neighbor.blue61 sum_green += neighbor.green62 pixel.red = sum_red /​ 663 pixel.blue = sum_blue /​ 664 pixel.green = sum_green /​ 665 elif y == 0:66 if x == img.width-1:67 for i in range(-1, 1):68 for j in range(0, 2):69 neighbor = img.get_pixel(x + i, y + j)70 sum_red += neighbor.red71 sum_blue += neighbor.blue72 sum_green += neighbor.green73 pixel.red = sum_red /​ 474 pixel.blue = sum_blue /​ 475 pixel.green = sum_green /​ 476 else:77 for i in range(-1, 2):78 for j in range(0, 2):79 neighbor = img.get_pixel(x + i, y + j)80 sum_red += neighbor.red81 sum_blue += neighbor.blue82 sum_green += neighbor.green83 pixel.red = sum_red /​ 684 pixel.blue = sum_blue /​ 685 pixel.green = sum_green /​ 686 elif x == img.width-1:87 if y == img.height-1:88 for i in range(-1, 1):89 for j in range(-1, 1):90 neighbor = img.get_pixel(x + i, y + j)91 sum_red += neighbor.red92 sum_blue += neighbor.blue93 sum_green += neighbor.green94 pixel.red = sum_red /​ 495 pixel.blue = sum_blue /​ 496 pixel.green = sum_green /​ 497 else:98 for i in range(-1, 1):99 for j in range(-1, 2):100 neighbor = img.get_pixel(x + i, y + j)101 sum_red += neighbor.red102 sum_blue += neighbor.blue103 sum_green += neighbor.green104 pixel.red = sum_red /​ 6105 pixel.blue = sum_blue /​ 6106 pixel.green = sum_green /​ 6107 elif y == img.height-1:108 for i in range(-1, 2):109 for j in range(-1, 1):110 neighbor = img.get_pixel(x + i, y + j)111 sum_red += neighbor.red112 sum_blue += neighbor.blue113 sum_green += neighbor.green114 pixel.red = sum_red /​ 6115 pixel.blue = sum_blue /​ 6116 pixel.green = sum_green /​ 6117 else:118 for i in range(-1, 2):119 for j in range(-1, 2):120 neighbor = img.get_pixel(x+i, y+j)121 sum_red += neighbor.red122 sum_blue += neighbor.blue123 sum_green += neighbor.green124 pixel.red = sum_red/​9125 pixel.blue = sum_blue/​9126 pixel.green = sum_green/​9127 return new_img128# ---- DO NOT EDIT CODE BELOW THIS LINE ---- #129if __name__ == '__main__':...

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