shamir's trick

core/ecc.js

@@ -29,6 +29,30 @@ sjcl.ecc.point.prototype = {
     return this.toJac().mult(k, this).toAffine();
   },
   
+  /**
+   * Multiply this point by k, added to affine2*k2, and return the answer in Jacobian coordinates.
+   * @param {bigInt} k The coefficient to multiply this by.
+   * @param {bigInt} k2 The coefficient to multiply affine2 this by.
+   * @param {sjcl.ecc.point} affine The other point in affine coordinates.
+   * @return {sjcl.ecc.pointJac} The result of the multiplication and addition, in Jacobian coordinates.
+   */
+  mult2: function(k, k2, affine2) {
+    return this.toJac().mult2(k, this, k2, affine2).toAffine();
+  },
+  
+  multiples: function() {
+    var m, i, j;
+    if (this._multiples === undefined) {
+      j = this.toJac().doubl();
+      m = this._multiples = [new sjcl.ecc.point(this.curve), this, j.toAffine()];
+      for (i=3; i<16; i++) {
+        j = j.add(this);
+        m.push(j.toAffine());
+      }
+    }
+    return this._multiples;
+  },
+
   isValid: function() {
     return this.y.square().equals(this.curve.b.add(this.x.mul(this.curve.a.add(this.x.square()))));
   },
@@ -156,21 +180,8 @@ sjcl.ecc.pointJac.prototype = {
     } else if (k.limbs !== undefined) {
       k = k.normalize().limbs;
     }
-    var i, j, out = new sjcl.ecc.point(this.curve).toJac(), multiples, aff2;
     
-    if (affine === undefined) {
+    var i, j, out = new sjcl.ecc.point(this.curve).toJac(), multiples = affine.multiples();
-      affine = this.toAffine();
-    }
-
-    if (affine.multiples === undefined) {
-      j = this.doubl();
-      affine.multiples = [new sjcl.ecc.point(this.curve), affine, j.toAffine()];
-      for (i=3; i<16; i++) {
-        j = j.add(affine);
-        affine.multiples[i] = j.toAffine();
-      }
-    }
-    multiples = affine.multiples;
 
     for (i=k.length-1; i>=0; i--) {
       for (j=sjcl.bn.prototype.radix-4; j>=0; j-=4) {
@@ -181,6 +192,41 @@ sjcl.ecc.pointJac.prototype = {
     return out;
   },
   
+  /**
+   * Multiply this point by k, added to affine2*k2, and return the answer in Jacobian coordinates.
+   * @param {bigInt} k The coefficient to multiply this by.
+   * @param {sjcl.ecc.point} affine This point in affine coordinates.
+   * @param {bigInt} k2 The coefficient to multiply affine2 this by.
+   * @param {sjcl.ecc.point} affine The other point in affine coordinates.
+   * @return {sjcl.ecc.pointJac} The result of the multiplication and addition, in Jacobian coordinates.
+   */
+  mult2: function(k1, affine, k2, affine2) {
+    if (typeof(k1) == "number") {
+      k1 = [k1];
+    } else if (k1.limbs !== undefined) {
+      k1 = k1.normalize().limbs;
+    }
+    
+    if (typeof(k2) == "number") {
+      k2 = [k2];
+    } else if (k2.limbs !== undefined) {
+      k2 = k2.normalize().limbs;
+    }
+    
+    var i, j, out = new sjcl.ecc.point(this.curve).toJac(), m1 = affine.multiples(),
+        m2 = affine2.multiples(), l1, l2;
+
+    for (i=Math.max(k1.length,k2.length)-1; i>=0; i--) {
+      l1 = k1[i] | 0;
+      l2 = k2[i] | 0;
+      for (j=sjcl.bn.prototype.radix-4; j>=0; j-=4) {
+        out = out.doubl().doubl().doubl().doubl().add(m1[l1>>j & 0xF]).add(m2[l2>>j & 0xF]);
+      }
+    }
+    
+    return out;
+  },
+
   isValid: function() {
     var z2 = this.z.square(), z4 = z2.square(), z6 = z4.mul(z2);
     return this.y.square().equals(
@@ -322,8 +368,7 @@ sjcl.ecc.dsa.publicKey.prototype = {
         s = sjcl.bn.fromBits(w.bitSlice(rs,l,2*l)),
         hG = sjcl.bn.fromBits(hash).mul(s).mod(R),
         hA = r.mul(s).mod(R),
-        jG = this._curve.G.toJac(),
+        r2 = this._curve.G.mult2(hG, hA, this._point).x,
-        r2 = jG.mult(hG, this._curve.G).add(this._point.mult(hA)).toAffine().x,
         corrupt = sjcl.exception.corrupt;
         
     if (r.equals(0) || s.equals(0) || r.greaterEquals(R) || s.greaterEquals(R) || !r2.equals(r)) {

sjcl.js

@@ -4,9 +4,9 @@ g[3][f[c&255]]}};
 sjcl.cipher.aes.prototype={encrypt:function(a){return this.O(a,0)},decrypt:function(a){return this.O(a,1)},l:[[[],[],[],[],[]],[[],[],[],[],[]]],F:function(){var a=this.l[0],b=this.l[1],c=a[4],d=b[4],e,f,g,h=[],j=[],n,l,m,o;for(e=0;e<0x100;e++)j[(h[e]=e<<1^(e>>7)*283)^e]=e;for(f=g=0;!c[f];f^=n||1,g=j[g]||1){m=g^g<<1^g<<2^g<<3^g<<4;m=m>>8^m&255^99;c[f]=m;d[m]=f;l=h[e=h[n=h[f]]];o=l*0x1010101^e*0x10001^n*0x101^f*0x1010100;l=h[m]*0x101^m*0x1010100;for(e=0;e<4;e++){a[e][f]=l=l<<24^l>>>8;b[e][m]=o=o<<24^o>>>8}}for(e=
 0;e<5;e++){a[e]=a[e].slice(0);b[e]=b[e].slice(0)}},O:function(a,b){if(a.length!==4)throw new sjcl.exception.invalid("invalid aes block size");var c=this.c[b],d=a[0]^c[0],e=a[b?3:1]^c[1],f=a[2]^c[2];a=a[b?1:3]^c[3];var g,h,j,n=c.length/4-2,l,m=4,o=[0,0,0,0];g=this.l[b];var q=g[0],r=g[1],s=g[2],t=g[3],u=g[4];for(l=0;l<n;l++){g=q[d>>>24]^r[e>>16&255]^s[f>>8&255]^t[a&255]^c[m];h=q[e>>>24]^r[f>>16&255]^s[a>>8&255]^t[d&255]^c[m+1];j=q[f>>>24]^r[a>>16&255]^s[d>>8&255]^t[e&255]^c[m+2];a=q[a>>>24]^r[d>>16&
 255]^s[e>>8&255]^t[f&255]^c[m+3];m+=4;d=g;e=h;f=j}for(l=0;l<4;l++){o[b?3&-l:l]=u[d>>>24]<<24^u[e>>16&255]<<16^u[f>>8&255]<<8^u[a&255]^c[m++];g=d;d=e;e=f;f=a;a=g}return o}};
-sjcl.bitArray={bitSlice:function(a,b,c){a=sjcl.bitArray.Z(a.slice(b/32),32-(b&31)).slice(1);return c===undefined?a:sjcl.bitArray.clamp(a,c-b)},extract:function(a,b,c){var d=-b-c&31;return((b+c-1^b)&-32?a[b/32|0]<<32-d^a[b/32+1|0]>>>d:a[b/32|0]>>>d)&(1<<c)-1},concat:function(a,b){if(a.length===0||b.length===0)return a.concat(b);var c=a[a.length-1],d=sjcl.bitArray.getPartial(c);return d===32?a.concat(b):sjcl.bitArray.Z(b,d,c|0,a.slice(0,a.length-1))},bitLength:function(a){var b=a.length;if(b===0)return 0;
+sjcl.bitArray={bitSlice:function(a,b,c){a=sjcl.bitArray.$(a.slice(b/32),32-(b&31)).slice(1);return c===undefined?a:sjcl.bitArray.clamp(a,c-b)},extract:function(a,b,c){var d=-b-c&31;return((b+c-1^b)&-32?a[b/32|0]<<32-d^a[b/32+1|0]>>>d:a[b/32|0]>>>d)&(1<<c)-1},concat:function(a,b){if(a.length===0||b.length===0)return a.concat(b);var c=a[a.length-1],d=sjcl.bitArray.getPartial(c);return d===32?a.concat(b):sjcl.bitArray.$(b,d,c|0,a.slice(0,a.length-1))},bitLength:function(a){var b=a.length;if(b===0)return 0;
 return(b-1)*32+sjcl.bitArray.getPartial(a[b-1])},clamp:function(a,b){if(a.length*32<b)return a;a=a.slice(0,Math.ceil(b/32));var c=a.length;b&=31;if(c>0&&b)a[c-1]=sjcl.bitArray.partial(b,a[c-1]&2147483648>>b-1,1);return a},partial:function(a,b,c){if(a===32)return b;return(c?b|0:b<<32-a)+a*0x10000000000},getPartial:function(a){return Math.round(a/0x10000000000)||32},equal:function(a,b){if(sjcl.bitArray.bitLength(a)!==sjcl.bitArray.bitLength(b))return false;var c=0,d;for(d=0;d<a.length;d++)c|=a[d]^b[d];
-return c===0},Z:function(a,b,c,d){var e;e=0;if(d===undefined)d=[];for(;b>=32;b-=32){d.push(c);c=0}if(b===0)return d.concat(a);for(e=0;e<a.length;e++){d.push(c|a[e]>>>b);c=a[e]<<32-b}e=a.length?a[a.length-1]:0;a=sjcl.bitArray.getPartial(e);d.push(sjcl.bitArray.partial(b+a&31,b+a>32?c:d.pop(),1));return d},o:function(a,b){return[a[0]^b[0],a[1]^b[1],a[2]^b[2],a[3]^b[3]]}};
+return c===0},$:function(a,b,c,d){var e;e=0;if(d===undefined)d=[];for(;b>=32;b-=32){d.push(c);c=0}if(b===0)return d.concat(a);for(e=0;e<a.length;e++){d.push(c|a[e]>>>b);c=a[e]<<32-b}e=a.length?a[a.length-1]:0;a=sjcl.bitArray.getPartial(e);d.push(sjcl.bitArray.partial(b+a&31,b+a>32?c:d.pop(),1));return d},o:function(a,b){return[a[0]^b[0],a[1]^b[1],a[2]^b[2],a[3]^b[3]]}};
 sjcl.codec.utf8String={fromBits:function(a){var b="",c=sjcl.bitArray.bitLength(a),d,e;for(d=0;d<c/8;d++){if((d&3)===0)e=a[d/4];b+=String.fromCharCode(e>>>24);e<<=8}return decodeURIComponent(escape(b))},toBits:function(a){a=unescape(encodeURIComponent(a));var b=[],c,d=0;for(c=0;c<a.length;c++){d=d<<8|a.charCodeAt(c);if((c&3)===3){b.push(d);d=0}}c&3&&b.push(sjcl.bitArray.partial(8*(c&3),d));return b}};
 sjcl.codec.hex={fromBits:function(a){var b="",c;for(c=0;c<a.length;c++)b+=((a[c]|0)+0xf00000000000).toString(16).substr(4);return b.substr(0,sjcl.bitArray.bitLength(a)/4)},toBits:function(a){var b,c=[],d;a=a.replace(/\s|0x/g,"");d=a.length;a+="00000000";for(b=0;b<a.length;b+=8)c.push(parseInt(a.substr(b,8),16)^0);return sjcl.bitArray.clamp(c,d*4)}};
 sjcl.codec.base64={L:"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/",fromBits:function(a,b){var c="",d,e=0,f=sjcl.codec.base64.L,g=0,h=sjcl.bitArray.bitLength(a);for(d=0;c.length*6<h;){c+=f.charAt((g^a[d]>>>e)>>>26);if(e<6){g=a[d]<<6-e;e+=26;d++}else{g<<=6;e-=6}}for(;c.length&3&&!b;)c+="=";return c},toBits:function(a){a=a.replace(/\s|=/g,"");var b=[],c,d=0,e=sjcl.codec.base64.L,f=0,g;for(c=0;c<a.length;c++){g=e.indexOf(a.charAt(c));if(g<0)throw new sjcl.exception.invalid("this isn't base64!");
@@ -23,20 +23,20 @@ n(l,f?d:sjcl.mode.ocb2.pmac(a,d));return o.concat(j.concat(m,j.clamp(l,e)))},dec
 o));n=j(n,m);n=a.encrypt(j(n,j(l,g(l))));if(d.length)n=j(n,f?d:sjcl.mode.ocb2.pmac(a,d));if(!h.equal(h.clamp(n,e),h.bitSlice(b,q)))throw new sjcl.exception.corrupt("ocb: tag doesn't match");return r.concat(h.clamp(m,o))},pmac:function(a,b){var c,d=sjcl.mode.ocb2.I,e=sjcl.bitArray,f=e.o,g=[0,0,0,0],h=a.encrypt([0,0,0,0]);h=f(h,d(d(h)));for(c=0;c+4<b.length;c+=4){h=d(h);g=f(g,a.encrypt(f(h,b.slice(c,c+4))))}b=b.slice(c);if(e.bitLength(b)<128){h=f(h,d(h));b=e.concat(b,[2147483648|0])}g=f(g,b);return a.encrypt(f(d(f(h,
 d(h))),g))},I:function(a){return[a[0]<<1^a[1]>>>31,a[1]<<1^a[2]>>>31,a[2]<<1^a[3]>>>31,a[3]<<1^(a[0]>>>31)*135]}};sjcl.misc.hmac=function(a,b){this.V=b=b||sjcl.hash.sha256;var c=[[],[]],d=b.prototype.blockSize/32;this.p=[new b,new b];if(a.length>d)a=b.hash(a);for(b=0;b<d;b++){c[0][b]=a[b]^909522486;c[1][b]=a[b]^1549556828}this.p[0].update(c[0]);this.p[1].update(c[1])};sjcl.misc.hmac.prototype.encrypt=sjcl.misc.hmac.prototype.mac=function(a,b){a=(new this.V(this.p[0])).update(a,b).finalize();return(new this.V(this.p[1])).update(a).finalize()};
 sjcl.misc.pbkdf2=function(a,b,c,d,e){c=c||1E3;if(d<0||c<0)throw sjcl.exception.invalid("invalid params to pbkdf2");if(typeof a==="string")a=sjcl.codec.utf8String.toBits(a);e=e||sjcl.misc.hmac;a=new e(a);var f,g,h,j,n=[],l=sjcl.bitArray;for(j=1;32*n.length<(d||1);j++){e=f=a.encrypt(l.concat(b,[j]));for(g=1;g<c;g++){f=a.encrypt(f);for(h=0;h<f.length;h++)e[h]^=f[h]}n=n.concat(e)}if(d)n=l.clamp(n,d);return n};
-sjcl.random={randomWords:function(a,b){var c=[];b=this.isReady(b);var d;if(b===0)throw new sjcl.exception.notReady("generator isn't seeded");else b&2&&this.ea(!(b&1));for(b=0;b<a;b+=4){(b+1)%0x10000===0&&this.U();d=this.D();c.push(d[0],d[1],d[2],d[3])}this.U();return c.slice(0,a)},setDefaultParanoia:function(a){this.C=a},addEntropy:function(a,b,c){c=c||"user";var d,e,f=(new Date).valueOf(),g=this.w[c],h=this.isReady();d=this.M[c];if(d===undefined)d=this.M[c]=this.ba++;if(g===undefined)g=this.w[c]=0;
+sjcl.random={randomWords:function(a,b){var c=[];b=this.isReady(b);var d;if(b===0)throw new sjcl.exception.notReady("generator isn't seeded");else b&2&&this.fa(!(b&1));for(b=0;b<a;b+=4){(b+1)%0x10000===0&&this.U();d=this.D();c.push(d[0],d[1],d[2],d[3])}this.U();return c.slice(0,a)},setDefaultParanoia:function(a){this.C=a},addEntropy:function(a,b,c){c=c||"user";var d,e,f=(new Date).valueOf(),g=this.w[c],h=this.isReady();d=this.M[c];if(d===undefined)d=this.M[c]=this.ca++;if(g===undefined)g=this.w[c]=0;
 this.w[c]=(this.w[c]+1)%this.f.length;switch(typeof a){case "number":break;case "object":if(b===undefined)for(c=b=0;c<a.length;c++)for(e=a[c];e>0;){b++;e>>>=1}this.f[g].update([d,this.R++,2,b,f,a.length].concat(a));break;case "string":if(b===undefined)b=a.length;this.f[g].update([d,this.R++,3,b,f,a.length]);this.f[g].update(a);break;default:throw new sjcl.exception.bug("random: addEntropy only supports number, array or string");}this.n[g]+=b;this.j+=b;if(h===0){this.isReady()!==0&&this.T("seeded",
-Math.max(this.k,this.j));this.T("progress",this.getProgress())}},isReady:function(a){a=this.J[a!==undefined?a:this.C];return this.k&&this.k>=a?this.n[0]>80&&(new Date).valueOf()>this.X?3:1:this.j>=a?2:0},getProgress:function(a){a=this.J[a?a:this.C];return this.k>=a?1["0"]:this.j>a?1["0"]:this.j/a},startCollectors:function(){if(!this.q){if(window.addEventListener){window.addEventListener("load",this.t,false);window.addEventListener("mousemove",this.u,false)}else if(document.attachEvent){document.attachEvent("onload",
+Math.max(this.k,this.j));this.T("progress",this.getProgress())}},isReady:function(a){a=this.J[a!==undefined?a:this.C];return this.k&&this.k>=a?this.n[0]>80&&(new Date).valueOf()>this.Y?3:1:this.j>=a?2:0},getProgress:function(a){a=this.J[a?a:this.C];return this.k>=a?1["0"]:this.j>a?1["0"]:this.j/a},startCollectors:function(){if(!this.q){if(window.addEventListener){window.addEventListener("load",this.t,false);window.addEventListener("mousemove",this.u,false)}else if(document.attachEvent){document.attachEvent("onload",
-this.t);document.attachEvent("onmousemove",this.u)}else throw new sjcl.exception.bug("can't attach event");this.q=true}},stopCollectors:function(){if(this.q){if(window.removeEventListener){window.removeEventListener("load",this.t);window.removeEventListener("mousemove",this.u)}else if(window.detachEvent){window.detachEvent("onload",this.t);window.detachEvent("onmousemove",this.u)}this.q=false}},addEventListener:function(a,b){this.A[a][this.aa++]=b},removeEventListener:function(a,b){var c;a=this.A[a];
+this.t);document.attachEvent("onmousemove",this.u)}else throw new sjcl.exception.bug("can't attach event");this.q=true}},stopCollectors:function(){if(this.q){if(window.removeEventListener){window.removeEventListener("load",this.t);window.removeEventListener("mousemove",this.u)}else if(window.detachEvent){window.detachEvent("onload",this.t);window.detachEvent("onmousemove",this.u)}this.q=false}},addEventListener:function(a,b){this.A[a][this.ba++]=b},removeEventListener:function(a,b){var c;a=this.A[a];
-var d=[];for(c in a)a.hasOwnProperty[c]&&a[c]===b&&d.push(c);for(b=0;b<d.length;b++){c=d[b];delete a[c]}},f:[new sjcl.hash.sha256],n:[0],H:0,w:{},R:0,M:{},ba:0,k:0,j:0,X:0,c:[0,0,0,0,0,0,0,0],h:[0,0,0,0],B:undefined,C:6,q:false,A:{progress:{},seeded:{}},aa:0,J:[0,48,64,96,128,192,0x100,384,512,768,1024],D:function(){for(var a=0;a<4;a++){this.h[a]=this.h[a]+1|0;if(this.h[a])break}return this.B.encrypt(this.h)},U:function(){this.c=this.D().concat(this.D());this.B=new sjcl.cipher.aes(this.c)},da:function(a){this.c=
+var d=[];for(c in a)a.hasOwnProperty[c]&&a[c]===b&&d.push(c);for(b=0;b<d.length;b++){c=d[b];delete a[c]}},f:[new sjcl.hash.sha256],n:[0],H:0,w:{},R:0,M:{},ca:0,k:0,j:0,Y:0,c:[0,0,0,0,0,0,0,0],h:[0,0,0,0],B:undefined,C:6,q:false,A:{progress:{},seeded:{}},ba:0,J:[0,48,64,96,128,192,0x100,384,512,768,1024],D:function(){for(var a=0;a<4;a++){this.h[a]=this.h[a]+1|0;if(this.h[a])break}return this.B.encrypt(this.h)},U:function(){this.c=this.D().concat(this.D());this.B=new sjcl.cipher.aes(this.c)},ea:function(a){this.c=
-sjcl.hash.sha256.hash(this.c.concat(a));this.B=new sjcl.cipher.aes(this.c);for(a=0;a<4;a++){this.h[a]=this.h[a]+1|0;if(this.h[a])break}},ea:function(a){var b=[],c=0,d;this.X=b[0]=(new Date).valueOf()+3E4;for(d=0;d<16;d++)b.push(Math.random()*0x100000000|0);for(d=0;d<this.f.length;d++){b=b.concat(this.f[d].finalize());c+=this.n[d];this.n[d]=0;if(!a&&this.H&1<<d)break}if(this.H>=1<<this.f.length){this.f.push(new sjcl.hash.sha256);this.n.push(0)}this.j-=c;if(c>this.k)this.k=c;this.H++;this.da(b)},u:function(a){sjcl.random.addEntropy([a.x||
+sjcl.hash.sha256.hash(this.c.concat(a));this.B=new sjcl.cipher.aes(this.c);for(a=0;a<4;a++){this.h[a]=this.h[a]+1|0;if(this.h[a])break}},fa:function(a){var b=[],c=0,d;this.Y=b[0]=(new Date).valueOf()+3E4;for(d=0;d<16;d++)b.push(Math.random()*0x100000000|0);for(d=0;d<this.f.length;d++){b=b.concat(this.f[d].finalize());c+=this.n[d];this.n[d]=0;if(!a&&this.H&1<<d)break}if(this.H>=1<<this.f.length){this.f.push(new sjcl.hash.sha256);this.n.push(0)}this.j-=c;if(c>this.k)this.k=c;this.H++;this.ea(b)},u:function(a){sjcl.random.addEntropy([a.x||
 a.clientX||a.offsetX,a.y||a.clientY||a.offsetY],2,"mouse")},t:function(){sjcl.random.addEntropy(new Date,2,"loadtime")},T:function(a,b){var c;a=sjcl.random.A[a];var d=[];for(c in a)a.hasOwnProperty(c)&&d.push(a[c]);for(c=0;c<d.length;c++)d[c](b)}};
 sjcl.json={defaults:{v:1,iter:1E3,ks:128,ts:64,mode:"ccm",adata:"",cipher:"aes"},encrypt:function(a,b,c,d){c=c||{};d=d||{};var e=sjcl.json,f=e.g({iv:sjcl.random.randomWords(4,0)},e.defaults);e.g(f,c);if(typeof f.salt==="string")f.salt=sjcl.codec.base64.toBits(f.salt);if(typeof f.iv==="string")f.iv=sjcl.codec.base64.toBits(f.iv);if(!sjcl.mode[f.mode]||!sjcl.cipher[f.cipher]||typeof a==="string"&&f.iter<=100||f.ts!==64&&f.ts!==96&&f.ts!==128||f.ks!==128&&f.ks!==192&&f.ks!==0x100||f.iv.length<2||f.iv.length>
 4)throw new sjcl.exception.invalid("json encrypt: invalid parameters");if(typeof a==="string"){c=sjcl.misc.cachedPbkdf2(a,f);a=c.key.slice(0,f.ks/32);f.salt=c.salt}if(typeof b==="string")b=sjcl.codec.utf8String.toBits(b);c=new sjcl.cipher[f.cipher](a);e.g(d,f);d.key=a;f.ct=sjcl.mode[f.mode].encrypt(c,b,f.iv,f.adata,f.tag);return e.encode(f)},decrypt:function(a,b,c,d){c=c||{};d=d||{};var e=sjcl.json;b=e.g(e.g(e.g({},e.defaults),e.decode(b)),c,true);if(typeof b.salt==="string")b.salt=sjcl.codec.base64.toBits(b.salt);
 if(typeof b.iv==="string")b.iv=sjcl.codec.base64.toBits(b.iv);if(!sjcl.mode[b.mode]||!sjcl.cipher[b.cipher]||typeof a==="string"&&b.iter<=100||b.ts!==64&&b.ts!==96&&b.ts!==128||b.ks!==128&&b.ks!==192&&b.ks!==0x100||!b.iv||b.iv.length<2||b.iv.length>4)throw new sjcl.exception.invalid("json decrypt: invalid parameters");if(typeof a==="string"){c=sjcl.misc.cachedPbkdf2(a,b);a=c.key.slice(0,b.ks/32);b.salt=c.salt}c=new sjcl.cipher[b.cipher](a);c=sjcl.mode[b.mode].decrypt(c,b.ct,b.iv,b.adata,b.tag);e.g(d,
 b);d.key=a;return sjcl.codec.utf8String.fromBits(c)},encode:function(a){var b,c="{",d="";for(b in a)if(a.hasOwnProperty(b)){if(!b.match(/^[a-z0-9]+$/i))throw new sjcl.exception.invalid("json encode: invalid property name");c+=d+"'"+b+"':";d=",";switch(typeof a[b]){case "number":case "boolean":c+=a[b];break;case "string":c+='"'+escape(a[b])+'"';break;case "object":c+='"'+sjcl.codec.base64.fromBits(a[b],1)+'"';break;default:throw new sjcl.exception.bug("json encode: unsupported type");}}return c+"}"},
 decode:function(a){a=a.replace(/\s/g,"");if(!a.match(/^\{.*\}$/))throw new sjcl.exception.invalid("json decode: this isn't json!");a=a.replace(/^\{|\}$/g,"").split(/,/);var b={},c,d;for(c=0;c<a.length;c++){if(!(d=a[c].match(/^(?:(["']?)([a-z][a-z0-9]*)\1):(?:(\d+)|"([a-z0-9+\/%*_.@=\-]*)")$/i)))throw new sjcl.exception.invalid("json decode: this isn't json!");b[d[2]]=d[3]?parseInt(d[3],10):d[2].match(/^(ct|salt|iv)$/)?sjcl.codec.base64.toBits(d[4]):unescape(d[4])}return b},g:function(a,b,c){if(a===
-undefined)a={};if(b===undefined)return a;var d;for(d in b)if(b.hasOwnProperty(d)){if(c&&a[d]!==undefined&&a[d]!==b[d])throw new sjcl.exception.invalid("required parameter overridden");a[d]=b[d]}return a},fa:function(a,b){var c={},d;for(d=0;d<b.length;d++)if(a[b[d]]!==undefined)c[b[d]]=a[b[d]];return c}};sjcl.encrypt=sjcl.json.encrypt;sjcl.decrypt=sjcl.json.decrypt;sjcl.misc.ca={};
+undefined)a={};if(b===undefined)return a;var d;for(d in b)if(b.hasOwnProperty(d)){if(c&&a[d]!==undefined&&a[d]!==b[d])throw new sjcl.exception.invalid("required parameter overridden");a[d]=b[d]}return a},ga:function(a,b){var c={},d;for(d=0;d<b.length;d++)if(a[b[d]]!==undefined)c[b[d]]=a[b[d]];return c}};sjcl.encrypt=sjcl.json.encrypt;sjcl.decrypt=sjcl.json.decrypt;sjcl.misc.da={};
-sjcl.misc.cachedPbkdf2=function(a,b){var c=sjcl.misc.ca,d;b=b||{};d=b.iter||1E3;c=c[a]=c[a]||{};d=c[d]=c[d]||{firstSalt:b.salt&&b.salt.length?b.salt.slice(0):sjcl.random.randomWords(2,0)};c=b.salt===undefined?d.firstSalt:b.salt;d[c]=d[c]||sjcl.misc.pbkdf2(a,c,b.iter);return{key:d[c].slice(0),salt:c.slice(0)}};sjcl.bn=function(a){this.initWith(a)};
+sjcl.misc.cachedPbkdf2=function(a,b){var c=sjcl.misc.da,d;b=b||{};d=b.iter||1E3;c=c[a]=c[a]||{};d=c[d]=c[d]||{firstSalt:b.salt&&b.salt.length?b.salt.slice(0):sjcl.random.randomWords(2,0)};c=b.salt===undefined?d.firstSalt:b.salt;d[c]=d[c]||sjcl.misc.pbkdf2(a,c,b.iter);return{key:d[c].slice(0),salt:c.slice(0)}};sjcl.bn=function(a){this.initWith(a)};
 sjcl.bn.prototype={radix:24,maxMul:8,d:sjcl.bn,copy:function(){return new this.d(this)},initWith:function(a){var b=0,c;switch(typeof a){case "object":this.limbs=a.limbs.slice(0);break;case "number":this.limbs=[a];this.normalize();break;case "string":a=a.replace(/^0x/,"");this.limbs=[];c=this.radix/4;for(b=0;b<a.length;b+=c)this.limbs.push(parseInt(a.substring(Math.max(a.length-b-c,0),a.length-b),16));break;default:this.limbs=[0]}return this},equals:function(a){if(typeof a=="number")a=new this.d(a);
 var b=0,c;this.fullReduce();a.fullReduce();for(c=0;c<this.limbs.length||c<a.limbs.length;c++)b|=this.getLimb(c)^a.getLimb(c);return b===0},getLimb:function(a){return a>=this.limbs.length?0:this.limbs[a]},greaterEquals:function(a){if(typeof a=="number")a=new this.d(a);var b=0,c=0,d,e,f;for(d=Math.max(this.limbs.length,a.limbs.length)-1;d>=0;d--){e=this.getLimb(d);f=a.getLimb(d);c|=f-e&~b;b|=e-f&~c}return(c|~b)>>>31},toString:function(){this.fullReduce();var a="",b,c,d=this.limbs;for(b=0;b<this.limbs.length;b++){for(c=
 d[b].toString(16);b<this.limbs.length-1&&c.length<6;)c="0"+c;a=c+a}return"0x"+a},addM:function(a){if(typeof a!=="object")a=new this.d(a);var b=this.limbs,c=a.limbs;for(a=b.length;a<c.length;a++)b[a]=0;for(a=0;a<c.length;a++)b[a]+=c[a];return this},doubleM:function(){var a,b=0,c,d=this.radix,e=this.radixMask,f=this.limbs;for(a=0;a<f.length;a++){c=f[a];c=c+c+b;f[a]=c&e;b=c>>d}b&&f.push(b);return this},halveM:function(){var a,b=0,c,d=this.radix,e=this.limbs;for(a=e.length-1;a>=0;a--){c=e[a];e[a]=c+b>>
@@ -47,22 +47,23 @@ var b,c=new this.d(1),d=this;for(i=0;i<a.length;i++)for(b=0;b<this.radix;b++){if
 0,b,c=this.ipv,d,e=this.limbs,f=e.length,g=this.radixMask;for(b=0;b<f-1;b++){a=e[b]+a;d=e[b]=a&g;a=(a-d)*c}e[b]+=a;return this},toBits:function(a){this.fullReduce();a=a||this.exponent||this.limbs.length*this.radix;var b=Math.floor((a-1)/24),c=sjcl.bitArray;out=[c.partial((a+7&-8)%this.radix||this.radix,this.getLimb(b))];for(b--;b>=0;b--)out=c.concat(out,[c.partial(this.radix,this.getLimb(b))]);return out},bitLength:function(){this.fullReduce();for(var a=this.radix*(this.limbs.length-1),b=this.limbs[this.limbs.length-
 1];b;b>>=1)a++;return a+7&-8}};sjcl.bn.fromBits=function(a){var b=new this,c=[],d=sjcl.bitArray,e=this.prototype,f=Math.min(this.bitLength||0x100000000,d.bitLength(a)),g=f%e.radix||e.radix;for(c[0]=d.extract(a,0,g);g<f;g+=e.radix)c.unshift(d.extract(a,g,e.radix));b.limbs=c;return b};sjcl.bn.prototype.ipv=1/(sjcl.bn.prototype.placeVal=Math.pow(2,sjcl.bn.prototype.radix));sjcl.bn.prototype.radixMask=(1<<sjcl.bn.prototype.radix)-1;
 sjcl.bn.pseudoMersennePrime=function(a,b){function c(g){this.initWith(g)}var d=c.prototype=new sjcl.bn,e,f;e=d.modOffset=Math.ceil(f=a/d.radix);d.exponent=a;d.offset=[];d.factor=[];d.minOffset=e;d.fullMask=0;d.fullOffset=[];d.fullFactor=[];d.modulus=c.modulus=new sjcl.bn(Math.pow(2,a));d.fullMask=0|-Math.pow(2,a%d.radix);for(e=0;e<b.length;e++){d.offset[e]=Math.floor(b[e][0]/d.radix-f);d.fullOffset[e]=Math.ceil(b[e][0]/d.radix-f);d.factor[e]=b[e][1]*Math.pow(0.5,a-b[e][0]+d.offset[e]*d.radix);d.fullFactor[e]=
-b[e][1]*Math.pow(0.5,a-b[e][0]+d.fullOffset[e]*d.radix);d.modulus.addM(new sjcl.bn(Math.pow(2,b[e][0])*b[e][1]));d.minOffset=Math.min(d.minOffset,-d.offset[e])}d.d=c;d.modulus.cnormalize();d.reduce=function(){var g,h,j,n=this.modOffset,l=this.limbs,m=this.offset,o=this.offset.length,q=this.factor,r;for(g=this.minOffset;l.length>n;){j=l.pop();r=l.length;for(h=0;h<o;h++)l[r+m[h]]-=q[h]*j;g--;if(g==0){l.push(0);this.cnormalize();g=this.minOffset}}this.cnormalize();return this};d.$=d.fullMask==-1?d.reduce:
+b[e][1]*Math.pow(0.5,a-b[e][0]+d.fullOffset[e]*d.radix);d.modulus.addM(new sjcl.bn(Math.pow(2,b[e][0])*b[e][1]));d.minOffset=Math.min(d.minOffset,-d.offset[e])}d.d=c;d.modulus.cnormalize();d.reduce=function(){var g,h,j,n=this.modOffset,l=this.limbs,m=this.offset,o=this.offset.length,q=this.factor,r;for(g=this.minOffset;l.length>n;){j=l.pop();r=l.length;for(h=0;h<o;h++)l[r+m[h]]-=q[h]*j;g--;if(g==0){l.push(0);this.cnormalize();g=this.minOffset}}this.cnormalize();return this};d.aa=d.fullMask==-1?d.reduce:
-function(){var g=this.limbs,h=g.length-1,j;this.reduce();if(h==this.modOffset-1){j=g[h]&this.fullMask;g[h]-=j;for(k=0;k<this.fullOffset.length;k++)g[h+this.fullOffset[k]]-=this.fullFactor[k]*j;this.normalize()}};d.fullReduce=function(){var g,h;this.$();this.addM(this.modulus);this.addM(this.modulus);this.normalize();this.$();for(h=this.limbs.length;h<this.modOffset;h++)this.limbs[h]=0;g=this.greaterEquals(this.modulus);for(h=0;h<this.limbs.length;h++)this.limbs[h]-=this.modulus.limbs[h]*g;this.cnormalize();
+function(){var g=this.limbs,h=g.length-1,j;this.reduce();if(h==this.modOffset-1){j=g[h]&this.fullMask;g[h]-=j;for(k=0;k<this.fullOffset.length;k++)g[h+this.fullOffset[k]]-=this.fullFactor[k]*j;this.normalize()}};d.fullReduce=function(){var g,h;this.aa();this.addM(this.modulus);this.addM(this.modulus);this.normalize();this.aa();for(h=this.limbs.length;h<this.modOffset;h++)this.limbs[h]=0;g=this.greaterEquals(this.modulus);for(h=0;h<this.limbs.length;h++)this.limbs[h]-=this.modulus.limbs[h]*g;this.cnormalize();
 return this};d.inverse=function(){return this.power(this.modulus.sub(2))};c.fromBits=sjcl.bn.fromBits;return c};
 sjcl.bn.prime={p127:sjcl.bn.pseudoMersennePrime(127,[[0,-1]]),p25519:sjcl.bn.pseudoMersennePrime(255,[[0,-19]]),p192:sjcl.bn.pseudoMersennePrime(192,[[0,-1],[64,-1]]),p224:sjcl.bn.pseudoMersennePrime(224,[[0,1],[96,-1]]),p256:sjcl.bn.pseudoMersennePrime(0x100,[[0,-1],[96,1],[192,1],[224,-1]]),p384:sjcl.bn.pseudoMersennePrime(384,[[0,-1],[32,1],[96,-1],[128,-1]]),p521:sjcl.bn.pseudoMersennePrime(521,[[0,-1]])};
 sjcl.bn.random=function(a,b){if(typeof a!="object")a=new sjcl.bn(a);for(var c,d,e=a.limbs.length,f=a.limbs[e-1]+1,g=new sjcl.bn;;){do{c=sjcl.random.randomWords(e,b);if(c[e-1]<0)c[e-1]+=0x100000000}while(Math.floor(c[e-1]/f)==Math.floor(0x100000000/f));c[e-1]%=f;for(d=0;d<e-1;d++)c[d]&=a.radixMask;g.limbs=c;if(!g.greaterEquals(a))return g}};sjcl.ecc={};sjcl.ecc.point=function(a,b,c){if(b===undefined)this.isIdentity=true;else{this.x=b;this.y=c;this.isIdentity=false}this.curve=a};
-sjcl.ecc.point.prototype={toJac:function(){return new sjcl.ecc.pointJac(this.curve,this.x,this.y,new this.curve.field(1))},mult:function(a){return this.toJac().mult(a,this).toAffine()},isValid:function(){return this.y.square().equals(this.curve.b.add(this.x.mul(this.curve.a.add(this.x.square()))))},toBits:function(){return sjcl.bitArray.concat(this.x.toBits(),this.y.toBits())}};
+sjcl.ecc.point.prototype={toJac:function(){return new sjcl.ecc.pointJac(this.curve,this.x,this.y,new this.curve.field(1))},mult:function(a){return this.toJac().mult(a,this).toAffine()},mult2:function(a,b,c){return this.toJac().mult2(a,this,b,c).toAffine()},multiples:function(){var a,b,c;if(this.X===undefined){c=this.toJac().doubl();a=this.X=[new sjcl.ecc.point(this.curve),this,c.toAffine()];for(b=3;b<16;b++){c=c.add(this);a.push(c.toAffine())}}return this.X},isValid:function(){return this.y.square().equals(this.curve.b.add(this.x.mul(this.curve.a.add(this.x.square()))))},
-sjcl.ecc.pointJac=function(a,b,c,d){if(b===undefined)this.isIdentity=true;else{this.x=b;this.y=c;this.z=d;this.isIdentity=false}this.curve=a};
+toBits:function(){return sjcl.bitArray.concat(this.x.toBits(),this.y.toBits())}};sjcl.ecc.pointJac=function(a,b,c,d){if(b===undefined)this.isIdentity=true;else{this.x=b;this.y=c;this.z=d;this.isIdentity=false}this.curve=a};
 sjcl.ecc.pointJac.prototype={add:function(a){if(this.curve!==a.curve)throw"sjcl['ecc']['add'](): Points must be on the same curve to add them!";if(this.isIdentity)return a.toJac();else if(a.isIdentity)return this;var b=this.z.square(),c=a.x.mul(b).subM(this.x);if(c.equals(0))return this.y.equals(a.y.mul(b.mul(this.z)))?this.doubl():new sjcl.ecc.pointJac(this.curve);b=a.y.mul(b.mul(this.z)).subM(this.y);var d=c.square();a=b.square();var e=c.square().mul(c).addM(this.x.add(this.x).mul(d));a=a.subM(e);
 b=this.x.mul(d).subM(a).mul(b);d=this.y.mul(c.square().mul(c));b=b.subM(d);c=this.z.mul(c);c=new sjcl.ecc.pointJac(this.curve,a,b,c);if(!c.isValid())throw"FOOOOOOOO";return c},doubl:function(){if(this.isIdentity)return this;var a=this.y.square(),b=a.mul(this.x.mul(4)),c=a.square().mul(8);a=this.z.square();var d=this.x.sub(a).mul(3).mul(this.x.add(a));a=d.square().subM(b).subM(b);b=b.sub(a).mul(d).subM(c);c=this.y.add(this.y).mul(this.z);return new sjcl.ecc.pointJac(this.curve,a,b,c)},toAffine:function(){if(this.isIdentity||
-this.z.equals(0))return new sjcl.ecc.point(this.curve);var a=this.z.inverse(),b=a.square();return new sjcl.ecc.point(this.curve,this.x.mul(b).fullReduce(),this.y.mul(b.mul(a)).fullReduce())},mult:function(a,b){if(typeof a=="number")a=[a];else if(a.limbs!==undefined)a=a.normalize().limbs;var c,d,e=(new sjcl.ecc.point(this.curve)).toJac();if(b===undefined)b=this.toAffine();if(b.multiples===undefined){d=this.doubl();b.multiples=[new sjcl.ecc.point(this.curve),b,d.toAffine()];for(c=3;c<16;c++){d=d.add(b);
+this.z.equals(0))return new sjcl.ecc.point(this.curve);var a=this.z.inverse(),b=a.square();return new sjcl.ecc.point(this.curve,this.x.mul(b).fullReduce(),this.y.mul(b.mul(a)).fullReduce())},mult:function(a,b){if(typeof a=="number")a=[a];else if(a.limbs!==undefined)a=a.normalize().limbs;var c,d=(new sjcl.ecc.point(this.curve)).toJac(),e=b.multiples();for(b=a.length-1;b>=0;b--)for(c=sjcl.bn.prototype.radix-4;c>=0;c-=4)d=d.doubl().doubl().doubl().doubl().add(e[a[b]>>c&15]);return d},mult2:function(a,
-b.multiples[c]=d.toAffine()}}b=b.multiples;for(c=a.length-1;c>=0;c--)for(d=sjcl.bn.prototype.radix-4;d>=0;d-=4)e=e.doubl().doubl().doubl().doubl().add(b[a[c]>>d&15]);return e},isValid:function(){var a=this.z.square(),b=a.square();a=b.mul(a);return this.y.square().equals(this.curve.b.mul(a).add(this.x.mul(this.curve.a.mul(b).add(this.x.square()))))}};
+b,c,d){if(typeof a=="number")a=[a];else if(a.limbs!==undefined)a=a.normalize().limbs;if(typeof c=="number")c=[c];else if(c.limbs!==undefined)c=c.normalize().limbs;var e,f=(new sjcl.ecc.point(this.curve)).toJac();b=b.multiples();var g=d.multiples(),h,j;for(d=Math.max(a.length,c.length)-1;d>=0;d--){h=a[d]|0;j=c[d]|0;for(e=sjcl.bn.prototype.radix-4;e>=0;e-=4)f=f.doubl().doubl().doubl().doubl().add(b[h>>e&15]).add(g[j>>e&15])}return f},isValid:function(){var a=this.z.square(),b=a.square();a=b.mul(a);
-sjcl.ecc.curve=function(a,b,c,d,e,f){this.field=a;this.r=a.prototype.modulus.sub(b);this.a=new a(c);this.b=new a(d);this.G=new sjcl.ecc.point(this,new a(e),new a(f))};sjcl.ecc.curve.prototype.fromBits=function(a){var b=sjcl.bitArray,c=this.field.prototype.exponent+7&-8;p=new sjcl.ecc.point(this,this.field.fromBits(b.bitSlice(a,0,c)),this.field.fromBits(b.bitSlice(a,c,2*c)));if(!p.isValid())throw new sjcl.exception.corrupt("not on the curve!");return p};
+return this.y.square().equals(this.curve.b.mul(a).add(this.x.mul(this.curve.a.mul(b).add(this.x.square()))))}};sjcl.ecc.curve=function(a,b,c,d,e,f){this.field=a;this.r=a.prototype.modulus.sub(b);this.a=new a(c);this.b=new a(d);this.G=new sjcl.ecc.point(this,new a(e),new a(f))};
+sjcl.ecc.curve.prototype.fromBits=function(a){var b=sjcl.bitArray,c=this.field.prototype.exponent+7&-8;p=new sjcl.ecc.point(this,this.field.fromBits(b.bitSlice(a,0,c)),this.field.fromBits(b.bitSlice(a,c,2*c)));if(!p.isValid())throw new sjcl.exception.corrupt("not on the curve!");return p};
 sjcl.ecc.curves={c192:new sjcl.ecc.curve(sjcl.bn.prime.p192,"0x662107c8eb94364e4b2dd7ce",-3,"0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1","0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012","0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811"),c224:new sjcl.ecc.curve(sjcl.bn.prime.p224,"0xe95c1f470fc1ec22d6baa3a3d5c4",-3,"0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4","0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21","0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"),
 c256:new sjcl.ecc.curve(sjcl.bn.prime.p256,"0x4319055358e8617b0c46353d039cdaae",-3,"0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b","0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296","0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"),c384:new sjcl.ecc.curve(sjcl.bn.prime.p384,"0x389cb27e0bc8d21fa7e5f24cb74f58851313e696333ad68c",-3,"0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef","0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7",
 "0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f")};
-sjcl.ecc.Q=function(a){sjcl.ecc[a]={publicKey:function(b,c){this.e=b;this.Y=c instanceof Array?b.fromBits(c):c},secretKey:function(b,c){this.e=b;this.S=c},generateKeys:function(b,c){if(typeof b=="number"){b=sjcl.ecc.curves["c"+b];if(b===undefined)throw new sjcl.exception.invalid("no such curve");}c=sjcl.bn.random(b.r,c);var d=b.G.mult(c);return{pub:new sjcl.ecc[a].publicKey(b,d),sec:new sjcl.ecc[a].secretKey(b,c)}}}};sjcl.ecc.Q("elGamal");
+sjcl.ecc.Q=function(a){sjcl.ecc[a]={publicKey:function(b,c){this.e=b;this.Z=c instanceof Array?b.fromBits(c):c},secretKey:function(b,c){this.e=b;this.S=c},generateKeys:function(b,c){if(typeof b=="number"){b=sjcl.ecc.curves["c"+b];if(b===undefined)throw new sjcl.exception.invalid("no such curve");}c=sjcl.bn.random(b.r,c);var d=b.G.mult(c);return{pub:new sjcl.ecc[a].publicKey(b,d),sec:new sjcl.ecc[a].secretKey(b,c)}}}};sjcl.ecc.Q("elGamal");
-sjcl.ecc.elGamal.publicKey.prototype={kem:function(a){a=sjcl.bn.random(this.e.r,a);var b=this.e.G.mult(a).toBits();return{key:sjcl.hash.sha256.hash(this.Y.mult(a).toBits()),tag:b}}};sjcl.ecc.elGamal.secretKey.prototype={unkem:function(a){return sjcl.hash.sha256.hash(this.e.fromBits(a).mult(this.S).toBits())}};sjcl.ecc.Q("dsa");
+sjcl.ecc.elGamal.publicKey.prototype={kem:function(a){a=sjcl.bn.random(this.e.r,a);var b=this.e.G.mult(a).toBits();return{key:sjcl.hash.sha256.hash(this.Z.mult(a).toBits()),tag:b}}};sjcl.ecc.elGamal.secretKey.prototype={unkem:function(a){return sjcl.hash.sha256.hash(this.e.fromBits(a).mult(this.S).toBits())}};sjcl.ecc.Q("dsa");
 sjcl.ecc.dsa.secretKey.prototype={sign:function(a,b){var c=this.e.r,d=c.bitLength();b=this.e.G.mult(kkkk=sjcl.bn.random(c.sub(1),b).add(1)).x.mod(c);a=sjcl.bn.fromBits(a).add(b.mul(this.S)).inverseMod(c).mul(kkkk).mod(c);return sjcl.bitArray.concat(b.toBits(d),a.toBits(d))}};
-sjcl.ecc.dsa.publicKey.prototype={verify:function(a,b){var c=sjcl.bitArray,d=this.e.r,e=d.bitLength(),f=sjcl.bn.fromBits(c.bitSlice(b,0,e));b=sjcl.bn.fromBits(c.bitSlice(b,e,2*e));a=sjcl.bn.fromBits(a).mul(b).mod(d);c=f.mul(b).mod(d);a=this.e.G.toJac().mult(a,this.e.G).add(this.Y.mult(c)).toAffine().x;c=sjcl.exception.corrupt;if(f.equals(0)||b.equals(0)||f.greaterEquals(d)||b.greaterEquals(d)||!a.equals(f))throw new c("signature didn't check out");return true}};
+sjcl.ecc.dsa.publicKey.prototype={verify:function(a,b){var c=sjcl.bitArray,d=this.e.r,e=d.bitLength(),f=sjcl.bn.fromBits(c.bitSlice(b,0,e));b=sjcl.bn.fromBits(c.bitSlice(b,e,2*e));a=sjcl.bn.fromBits(a).mul(b).mod(d);c=f.mul(b).mod(d);a=this.e.G.mult2(a,c,this.Z).x;c=sjcl.exception.corrupt;if(f.equals(0)||b.equals(0)||f.greaterEquals(d)||b.greaterEquals(d)||!a.equals(f))throw new c("signature didn't check out");return true}};