0) {
if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
while(i >= 0) {
if(p < k) {
d = (this[i]&((1<>(p+=this.DB-k);
}
else {
d = (this[i]>>(p-=k))&km;
if(p <= 0) { p += this.DB; --i; }
}
if(d > 0) m = true;
if(m) r += int2char(d);
}
}
return m?r:"0";
}
// (public) -this
function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
// (public) |this|
function bnAbs() { return (this.s<0)?this.negate():this; }
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s-a.s;
if(r != 0) return r;
var i = this.t;
r = i-a.t;
if(r != 0) return r;
while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
return 0;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if((t=x>>>16) != 0) { x = t; r += 16; }
if((t=x>>8) != 0) { x = t; r += 8; }
if((t=x>>4) != 0) { x = t; r += 4; }
if((t=x>>2) != 0) { x = t; r += 2; }
if((t=x>>1) != 0) { x = t; r += 1; }
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if(this.t <= 0) return 0;
return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n,r) {
var i;
for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
for(i = n-1; i >= 0; --i) r[i] = 0;
r.t = this.t+n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n,r) {
for(var i = n; i < this.t; ++i) r[i-n] = this[i];
r.t = Math.max(this.t-n,0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n,r) {
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<= 0; --i) {
r[i+ds+1] = (this[i]>>cbs)|c;
c = (this[i]&bm)<= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t+ds+1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n,r) {
r.s = this.s;
var ds = Math.floor(n/this.DB);
if(ds >= this.t) { r.t = 0; return; }
var bs = n%this.DB;
var cbs = this.DB-bs;
var bm = (1<>bs;
for(var i = ds+1; i < this.t; ++i) {
r[i-ds-1] |= (this[i]&bm)<>bs;
}
if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<>= this.DB;
}
if(a.t < this.t) {
c -= a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c -= a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c<0)?-1:0;
if(c < -1) r[i++] = this.DV+c;
else if(c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a,r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i+y.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
r.s = 0;
r.clamp();
if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2*x.t;
while(--i >= 0) r[i] = 0;
for(i = 0; i < x.t-1; ++i) {
var c = x.am(i,x[i],r,2*i,0,1);
if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
r[i+x.t] -= x.DV;
r[i+x.t+1] = 1;
}
}
if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m,q,r) {
var pm = m.abs();
if(pm.t <= 0) return;
var pt = this.abs();
if(pt.t < pm.t) {
if(q != null) q.fromInt(0);
if(r != null) this.copyTo(r);
return;
}
if(r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB-nbits(pm[pm.t-1]); // normalize modulus
if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
else { pm.copyTo(y); pt.copyTo(r); }
var ys = y.t;
var y0 = y[ys-1];
if(y0 == 0) return;
var yt = y0*(1<1)?y[ys-2]>>this.F2:0);
var d1 = this.FV/yt, d2 = (1<= 0) {
r[r.t++] = 1;
r.subTo(t,r);
}
BigInteger.ONE.dlShiftTo(ys,t);
t.subTo(y,y); // "negative" y so we can replace sub with am later
while(y.t < ys) y[y.t++] = 0;
while(--j >= 0) {
// Estimate quotient digit
var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) { // Try it out
y.dlShiftTo(j,t);
r.subTo(t,r);
while(r[i] < --qd) r.subTo(t,r);
}
}
if(q != null) {
r.drShiftTo(ys,q);
if(ts != ms) BigInteger.ZERO.subTo(q,q);
}
r.t = ys;
r.clamp();
if(nsh > 0) r.rShiftTo(nsh,r); // Denormalize remainder
if(ts < 0) BigInteger.ZERO.subTo(r,r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs().divRemTo(a,null,r);
if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) { this.m = m; }
function cConvert(x) {
if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) { return x; }
function cReduce(x) { x.divRemTo(this.m,null,x); }
function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
if(this.t < 1) return 0;
var x = this[0];
if((x&1) == 0) return 0;
var y = x&3; // y == 1/x mod 2^2
y = (y*(2-(x&0xf)*y))&0xf; // y == 1/x mod 2^4
y = (y*(2-(x&0xff)*y))&0xff; // y == 1/x mod 2^8
y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff; // y == 1/x mod 2^16
// last step - calculate inverse mod DV directly;
// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
y = (y*(2-x*y%this.DV))%this.DV; // y == 1/x mod 2^dbits
// we really want the negative inverse, and -DV < y < DV
return (y>0)?this.DV-y:-y;
}
// Montgomery reduction
function Montgomery(m) {
this.m = m;
this.mp = m.invDigit();
this.mpl = this.mp&0x7fff;
this.mph = this.mp>>15;
this.um = (1<<(m.DB-15))-1;
this.mt2 = 2*m.t;
}
// xR mod m
function montConvert(x) {
var r = nbi();
x.abs().dlShiftTo(this.m.t,r);
r.divRemTo(this.m,null,r);
if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
return r;
}
// x/R mod m
function montRevert(x) {
var r = nbi();
x.copyTo(r);
this.reduce(r);
return r;
}
// x = x/R mod m (HAC 14.32)
function montReduce(x) {
while(x.t <= this.mt2) // pad x so am has enough room later
x[x.t++] = 0;
for(var i = 0; i < this.m.t; ++i) {
// faster way of calculating u0 = x[i]*mp mod DV
var j = x[i]&0x7fff;
var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
// use am to combine the multiply-shift-add into one call
j = i+this.m.t;
x[j] += this.m.am(0,u0,x,i,0,this.m.t);
// propagate carry
while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
}
x.clamp();
x.drShiftTo(this.m.t,x);
if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = "x^2/R mod m"; x != r
function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = "xy/R mod m"; x,y != r
function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Montgomery.prototype.convert = montConvert;
Montgomery.prototype.revert = montRevert;
Montgomery.prototype.reduce = montReduce;
Montgomery.prototype.mulTo = montMulTo;
Montgomery.prototype.sqrTo = montSqrTo;
// (protected) true iff this is even
function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
function bnpExp(e,z) {
if(e > 0xffffffff || e < 1) return BigInteger.ONE;
var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
g.copyTo(r);
while(--i >= 0) {
z.sqrTo(r,r2);
if((e&(1< 0) z.mulTo(r2,g,r);
else { var t = r; r = r2; r2 = t; }
}
return z.revert(r);
}
// (public) this^e % m, 0 <= e < 2^32
function bnModPowInt(e,m) {
var z;
if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
return this.exp(e,z);
}
// protected
BigInteger.prototype.copyTo = bnpCopyTo;
BigInteger.prototype.fromInt = bnpFromInt;
BigInteger.prototype.fromString = bnpFromString;
BigInteger.prototype.clamp = bnpClamp;
BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
BigInteger.prototype.drShiftTo = bnpDRShiftTo;
BigInteger.prototype.lShiftTo = bnpLShiftTo;
BigInteger.prototype.rShiftTo = bnpRShiftTo;
BigInteger.prototype.subTo = bnpSubTo;
BigInteger.prototype.multiplyTo = bnpMultiplyTo;
BigInteger.prototype.squareTo = bnpSquareTo;
BigInteger.prototype.divRemTo = bnpDivRemTo;
BigInteger.prototype.invDigit = bnpInvDigit;
BigInteger.prototype.isEven = bnpIsEven;
BigInteger.prototype.exp = bnpExp;
// public
BigInteger.prototype.toString = bnToString;
BigInteger.prototype.negate = bnNegate;
BigInteger.prototype.abs = bnAbs;
BigInteger.prototype.compareTo = bnCompareTo;
BigInteger.prototype.bitLength = bnBitLength;
BigInteger.prototype.mod = bnMod;
BigInteger.prototype.modPowInt = bnModPowInt;
// "constants"
BigInteger.ZERO = nbv(0);
BigInteger.ONE = nbv(1);
// Extended JavaScript BN functions, required for RSA private ops.
// (public)
function bnClone() { var r = nbi(); this.copyTo(r); return r; }
// (public) return value as integer
function bnIntValue() {
if(this.s < 0) {
if(this.t == 1) return this[0]-this.DV;
else if(this.t == 0) return -1;
}
else if(this.t == 1) return this[0];
else if(this.t == 0) return 0;
// assumes 16 < DB < 32
return ((this[1]&((1<<(32-this.DB))-1))<>24; }
// (public) return value as short (assumes DB>=16)
function bnShortValue() { return (this.t==0)?this.s:(this[0]<<16)>>16; }
// (protected) return x s.t. r^x < DV
function bnpChunkSize(r) { return Math.floor(Math.LN2*this.DB/Math.log(r)); }
// (public) 0 if this == 0, 1 if this > 0
function bnSigNum() {
if(this.s < 0) return -1;
else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
else return 1;
}
// (protected) convert to radix string
function bnpToRadix(b) {
if(b == null) b = 10;
if(this.signum() == 0 || b < 2 || b > 36) return "0";
var cs = this.chunkSize(b);
var a = Math.pow(b,cs);
var d = nbv(a), y = nbi(), z = nbi(), r = "";
this.divRemTo(d,y,z);
while(y.signum() > 0) {
r = (a+z.intValue()).toString(b).substr(1) + r;
y.divRemTo(d,y,z);
}
return z.intValue().toString(b) + r;
}
// (protected) convert from radix string
function bnpFromRadix(s,b) {
this.fromInt(0);
if(b == null) b = 10;
var cs = this.chunkSize(b);
var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
for(var i = 0; i < s.length; ++i) {
var x = intAt(s,i);
if(x < 0) {
if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
continue;
}
w = b*w+x;
if(++j >= cs) {
this.dMultiply(d);
this.dAddOffset(w,0);
j = 0;
w = 0;
}
}
if(j > 0) {
this.dMultiply(Math.pow(b,j));
this.dAddOffset(w,0);
}
if(mi) BigInteger.ZERO.subTo(this,this);
}
// (protected) alternate constructor
function bnpFromNumber(a,b,c) {
if("number" == typeof b) {
// new BigInteger(int,int,RNG)
if(a < 2) this.fromInt(1);
else {
this.fromNumber(a,c);
if(!this.testBit(a-1)) // force MSB set
this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
if(this.isEven()) this.dAddOffset(1,0); // force odd
while(!this.isProbablePrime(b)) {
this.dAddOffset(2,0);
if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
}
}
}
else {
// new BigInteger(int,RNG)
var x = new Array(), t = a&7;
x.length = (a>>3)+1;
b.nextBytes(x);
if(t > 0) x[0] &= ((1< 0) {
if(p < this.DB && (d = this[i]>>p) != (this.s&this.DM)>>p)
r[k++] = d|(this.s<<(this.DB-p));
while(i >= 0) {
if(p < 8) {
d = (this[i]&((1<>(p+=this.DB-8);
}
else {
d = (this[i]>>(p-=8))&0xff;
if(p <= 0) { p += this.DB; --i; }
}
if((d&0x80) != 0) d |= -256;
if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
if(k > 0 || d != this.s) r[k++] = d;
}
}
return r;
}
function bnEquals(a) { return(this.compareTo(a)==0); }
function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
// (protected) r = this op a (bitwise)
function bnpBitwiseTo(a,op,r) {
var i, f, m = Math.min(a.t,this.t);
for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
if(a.t < this.t) {
f = a.s&this.DM;
for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
r.t = this.t;
}
else {
f = this.s&this.DM;
for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
r.t = a.t;
}
r.s = op(this.s,a.s);
r.clamp();
}
// (public) this & a
function op_and(x,y) { return x&y; }
function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
// (public) this | a
function op_or(x,y) { return x|y; }
function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
// (public) this ^ a
function op_xor(x,y) { return x^y; }
function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
// (public) this & ~a
function op_andnot(x,y) { return x&~y; }
function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
// (public) ~this
function bnNot() {
var r = nbi();
for(var i = 0; i < this.t; ++i) r[i] = this.DM&~this[i];
r.t = this.t;
r.s = ~this.s;
return r;
}
// (public) this << n
function bnShiftLeft(n) {
var r = nbi();
if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
return r;
}
// (public) this >> n
function bnShiftRight(n) {
var r = nbi();
if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
return r;
}
// return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
if(x == 0) return -1;
var r = 0;
if((x&0xffff) == 0) { x >>= 16; r += 16; }
if((x&0xff) == 0) { x >>= 8; r += 8; }
if((x&0xf) == 0) { x >>= 4; r += 4; }
if((x&3) == 0) { x >>= 2; r += 2; }
if((x&1) == 0) ++r;
return r;
}
// (public) returns index of lowest 1-bit (or -1 if none)
function bnGetLowestSetBit() {
for(var i = 0; i < this.t; ++i)
if(this[i] != 0) return i*this.DB+lbit(this[i]);
if(this.s < 0) return this.t*this.DB;
return -1;
}
// return number of 1 bits in x
function cbit(x) {
var r = 0;
while(x != 0) { x &= x-1; ++r; }
return r;
}
// (public) return number of set bits
function bnBitCount() {
var r = 0, x = this.s&this.DM;
for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
return r;
}
// (public) true iff nth bit is set
function bnTestBit(n) {
var j = Math.floor(n/this.DB);
if(j >= this.t) return(this.s!=0);
return((this[j]&(1<<(n%this.DB)))!=0);
}
// (protected) this op (1<>= this.DB;
}
if(a.t < this.t) {
c += a.s;
while(i < this.t) {
c += this[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while(i < a.t) {
c += a[i];
r[i++] = c&this.DM;
c >>= this.DB;
}
c += a.s;
}
r.s = (c<0)?-1:0;
if(c > 0) r[i++] = c;
else if(c < -1) r[i++] = this.DV+c;
r.t = i;
r.clamp();
}
// (public) this + a
function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
// (public) this - a
function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
// (public) this * a
function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
// (public) this / a
function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
// (public) this % a
function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
// (public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this.divRemTo(a,q,r);
return new Array(q,r);
}
// (protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0,n-1,this,0,0,this.t);
++this.t;
this.clamp();
}
// (protected) this += n << w words, this >= 0
function bnpDAddOffset(n,w) {
while(this.t <= w) this[this.t++] = 0;
this[w] += n;
while(this[w] >= this.DV) {
this[w] -= this.DV;
if(++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
// A "null" reducer
function NullExp() {}
function nNop(x) { return x; }
function nMulTo(x,y,r) { x.multiplyTo(y,r); }
function nSqrTo(x,r) { x.squareTo(r); }
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
// (public) this^e
function bnPow(e) { return this.exp(e,new NullExp()); }
// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a,n,r) {
var i = Math.min(this.t+a.t,n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while(i > 0) r[--i] = 0;
var j;
for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
r.clamp();
}
// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a,n,r) {
--n;
var i = r.t = this.t+a.t-n;
r.s = 0; // assumes a,this >= 0
while(--i >= 0) r[i] = 0;
for(i = Math.max(n-this.t,0); i < a.t; ++i)
r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
r.clamp();
r.drShiftTo(1,r);
}
// Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
else if(x.compareTo(this.m) < 0) return x;
else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
}
function barrettRevert(x) { return x; }
// x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t-1,this.r2);
if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
x.subTo(this.r2,x);
while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
}
// r = x^2 mod m; x != r
function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
// r = x*y mod m; x,y != r
function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
// (public) this^e % m (HAC 14.85)
function bnModPow(e,m) {
var i = e.bitLength(), k, r = nbv(1), z;
if(i <= 0) return r;
else if(i < 18) k = 1;
else if(i < 48) k = 3;
else if(i < 144) k = 4;
else if(i < 768) k = 5;
else k = 6;
if(i < 8)
z = new Classic(m);
else if(m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = new Array(), n = 3, k1 = k-1, km = (1< 1) {
var g2 = nbi();
z.sqrTo(g[1],g2);
while(n <= km) {
g[n] = nbi();
z.mulTo(g2,g[n-2],g[n]);
n += 2;
}
}
var j = e.t-1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j])-1;
while(j >= 0) {
if(i >= k1) w = (e[j]>>(i-k1))&km;
else {
w = (e[j]&((1<<(i+1))-1))<<(k1-i);
if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
}
n = k;
while((w&1) == 0) { w >>= 1; --n; }
if((i -= n) < 0) { i += this.DB; --j; }
if(is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
z.mulTo(r2,g[w],r);
}
while(j >= 0 && (e[j]&(1< 0) {
x.rShiftTo(g,x);
y.rShiftTo(g,y);
}
while(x.signum() > 0) {
if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
if(x.compareTo(y) >= 0) {
x.subTo(y,x);
x.rShiftTo(1,x);
}
else {
y.subTo(x,y);
y.rShiftTo(1,y);
}
}
if(g > 0) y.lShiftTo(g,y);
return y;
}
// (protected) this % n, n < 2^26
function bnpModInt(n) {
if(n <= 0) return 0;
var d = this.DV%n, r = (this.s<0)?n-1:0;
if(this.t > 0)
if(d == 0) r = this[0]%n;
else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
return r;
}
// (public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while(u.signum() != 0) {
while(u.isEven()) {
u.rShiftTo(1,u);
if(ac) {
if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
a.rShiftTo(1,a);
}
else if(!b.isEven()) b.subTo(m,b);
b.rShiftTo(1,b);
}
while(v.isEven()) {
v.rShiftTo(1,v);
if(ac) {
if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
c.rShiftTo(1,c);
}
else if(!d.isEven()) d.subTo(m,d);
d.rShiftTo(1,d);
}
if(u.compareTo(v) >= 0) {
u.subTo(v,u);
if(ac) a.subTo(c,a);
b.subTo(d,b);
}
else {
v.subTo(u,v);
if(ac) c.subTo(a,c);
d.subTo(b,d);
}
}
if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if(d.compareTo(m) >= 0) return d.subtract(m);
if(d.signum() < 0) d.addTo(m,d); else return d;
if(d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];
// (public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
for(i = 0; i < lowprimes.length; ++i)
if(x[0] == lowprimes[i]) return true;
return false;
}
if(x.isEven()) return false;
i = 1;
while(i < lowprimes.length) {
var m = lowprimes[i], j = i+1;
while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while(i < j) if(m%lowprimes[i++] == 0) return false;
}
return x.millerRabin(t);
}
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if(k <= 0) return false;
var r = n1.shiftRight(k);
t = (t+1)>>1;
if(t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for(var i = 0; i < t; ++i) {
a.fromInt(lowprimes[i]);
var y = a.modPow(r,this);
if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while(j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2,this);
if(y.compareTo(BigInteger.ONE) == 0) return false;
}
if(y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
//HPM Security rng.js
//Author: Tom Wu
//tjw@cs.Stanford.EDU
//Random number generator - requires a PRNG backend, e.g. prng4.js
//For best results, put code like
//
//in your main HTML document.
function SecureRandom() {
this.rng_state;
this.rng_pool;
this.rng_pptr;
// Mix in a 32-bit integer into the pool
this.rng_seed_int = function(x) {
this.rng_pool[this.rng_pptr++] ^= x & 255;
this.rng_pool[this.rng_pptr++] ^= (x >> 8) & 255;
this.rng_pool[this.rng_pptr++] ^= (x >> 16) & 255;
this.rng_pool[this.rng_pptr++] ^= (x >> 24) & 255;
if(this.rng_pptr >= rng_psize) this.rng_pptr -= rng_psize;
}
// Mix in the current time (w/milliseconds) into the pool
this.rng_seed_time = function() {
this.rng_seed_int(new Date().getTime());
}
// Initialize the pool with junk if needed.
if(this.rng_pool == null) {
this.rng_pool = new Array();
this.rng_pptr = 0;
var t;
if(navigator.appName == "Netscape" && navigator.appVersion < "5" && window.crypto && window.crypto.random) {
// Extract entropy (256 bits) from NS4 RNG if available
var z = window.crypto.random(32);
for(t = 0; t < z.length; ++t)
this.rng_pool[this.rng_pptr++] = z.charCodeAt(t) & 255;
}
while(this.rng_pptr < rng_psize) { // extract some randomness from Math.random()
t = Math.floor(65536 * Math.random());
this.rng_pool[this.rng_pptr++] = t >>> 8;
this.rng_pool[this.rng_pptr++] = t & 255;
}
this.rng_pptr = 0;
this.rng_seed_time();
//this.rng_seed_int(window.screenX);
//this.rng_seed_int(window.screenY);
}
this.rng_get_byte = function() {
if(this.rng_state == null) {
this.rng_seed_time();
this.rng_state = prng_newstate();
this.rng_state.init(this.rng_pool);
for(this.rng_pptr = 0; this.rng_pptr < this.rng_pool.length; ++this.rng_pptr)
this.rng_pool[this.rng_pptr] = 0;
this.rng_pptr = 0;
//this.rng_pool = null;
}
// TODO: allow reseeding after first request
return this.rng_state.next();
}
//public function
this.nextBytes = function(ba) {
var i;
for(i = 0; i < ba.length; ++i) ba[i] = this.rng_get_byte();
}
}
//HPM Security prng4.js
//Author: Tom Wu
//tjw@cs.Stanford.EDU
//prng4.js - uses Arcfour as a PRNG
function Arcfour() {
this.i = 0;
this.j = 0;
this.S = new Array();
}
//Initialize arcfour context from key, an array of ints, each from [0..255]
function ARC4init(key) {
var i, j, t;
for(i = 0; i < 256; ++i)
this.S[i] = i;
j = 0;
for(i = 0; i < 256; ++i) {
j = (j + this.S[i] + key[i % key.length]) & 255;
t = this.S[i];
this.S[i] = this.S[j];
this.S[j] = t;
}
this.i = 0;
this.j = 0;
}
function ARC4next() {
var t;
this.i = (this.i + 1) & 255;
this.j = (this.j + this.S[this.i]) & 255;
t = this.S[this.i];
this.S[this.i] = this.S[this.j];
this.S[this.j] = t;
return this.S[(t + this.S[this.i]) & 255];
}
Arcfour.prototype.init = ARC4init;
Arcfour.prototype.next = ARC4next;
//Plug in your RNG constructor here
function prng_newstate() {
return new Arcfour();
}
//Pool size must be a multiple of 4 and greater than 32.
//An array of bytes the size of the pool will be passed to init()
var rng_psize = 256;
//HPM Security rsa.js
/*----------------------------------------------------------------------------*/
// Copyright (c) 2009 pidder
// Permission to use, copy, modify, and/or distribute this software for any
// purpose with or without fee is hereby granted, provided that the above
// copyright notice and this permission notice appear in all copies.
//
// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
// ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
// ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
// OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
/*----------------------------------------------------------------------------*/
/**
*
* PKCS#1 encryption-style padding (type 2) En- / Decryption for use in
* pidCrypt Library. The pidCrypt RSA module is based on the implementation
* by Tom Wu.
* See http://www-cs-students.stanford.edu/~tjw/jsbn/ for details and for his
* great job.
*
* Depends on pidCrypt (pidcrypt.js, pidcrypt_util.js), BigInteger (jsbn.js),
* random number generator (rng.js) and a PRNG backend (prng4.js) (the random
* number scripts are only needed for key generation).
/*----------------------------------------------------------------------------*/
/*
* Copyright (c) 2003-2005 Tom Wu
* All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
* EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
* WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
*
* IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
* INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
* RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
* THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
* OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*
* In addition, the following condition applies:
*
* All redistributions must retain an intact copy of this copyright notice
* and disclaimer.
*/
//Address all questions regarding this license to:
// Tom Wu
// tjw@cs.Stanford.EDU
/*----------------------------------------------------------------------------*/
if(typeof(pidCrypt) != 'undefined' &&
typeof(BigInteger) != 'undefined' &&//must have for rsa
typeof(SecureRandom) != 'undefined' &&//only needed for key generation
typeof(Arcfour) != 'undefined'//only needed for key generation
)
{
// Author: Tom Wu
// tjw@cs.Stanford.EDU
// convert a (hex) string to a bignum object
function parseBigInt(str,r) {
return new BigInteger(str,r);
}
function linebrk(s,n) {
var ret = "";
var i = 0;
while(i + n < s.length) {
ret += s.substring(i,i+n) + "\n";
i += n;
}
return ret + s.substring(i,s.length);
}
function byte2Hex(b) {
if(b < 0x10)
return "0" + b.toString(16);
else
return b.toString(16);
}
// Undo PKCS#1 (type 2, random) padding and, if valid, return the plaintext
function pkcs1unpad2(d,n) {
var b = d.toByteArray();
var i = 0;
while(i < b.length && b[i] == 0) ++i;
if(b.length-i != n-1 || b[i] != 2)
return null;
++i;
while(b[i] != 0)
if(++i >= b.length) return null;
var ret = "";
while(++i < b.length)
ret += String.fromCharCode(b[i]);
return ret;
}
// PKCS#1 (type 2, random) pad input string s to n bytes, and return a bigint
function pkcs1pad2(s,n) {
if(n < s.length + 11) {
alert("Message too long for RSA");
return null;
}
var ba = new Array();
var i = s.length - 1;
while(i >= 0 && n > 0) {ba[--n] = s.charCodeAt(i--);};
ba[--n] = 0;
var rng = new SecureRandom();
var x = new Array();
while(n > 2) { // random non-zero pad
x[0] = 0;
while(x[0] == 0) rng.nextBytes(x);
ba[--n] = x[0];
}
ba[--n] = 2;
ba[--n] = 0;
return new BigInteger(ba);
}
//RSA key constructor
pidCrypt.RSA = function() {
this.n = null;
this.e = 0;
this.d = null;
this.p = null;
this.q = null;
this.dmp1 = null;
this.dmq1 = null;
this.coeff = null;
}
// protected
// Perform raw private operation on "x": return x^d (mod n)
pidCrypt.RSA.prototype.doPrivate = function(x) {
if(this.p == null || this.q == null)
return x.modPow(this.d, this.n);
// TODO: re-calculate any missing CRT params
var xp = x.mod(this.p).modPow(this.dmp1, this.p);
var xq = x.mod(this.q).modPow(this.dmq1, this.q);
while(xp.compareTo(xq) < 0)
xp = xp.add(this.p);
return xp.subtract(xq).multiply(this.coeff).mod(this.p).multiply(this.q).add(xq);
}
// Set the public key fields N and e from hex strings
pidCrypt.RSA.prototype.setPublic = function(N,E,radix) {
if (typeof(radix) == 'undefined') radix = 16;
if(N != null && E != null && N.length > 0 && E.length > 0) {
this.n = parseBigInt(N,radix);
this.e = parseInt(E,radix);
}
else
alert("Invalid RSA public key");
// alert('N='+this.n+'\nE='+this.e);
//document.writeln('Schlüssellaenge = ' + this.n.toString().length +'
');
}
// Perform raw public operation on "x": return x^e (mod n)
pidCrypt.RSA.prototype.doPublic = function(x) {
return x.modPowInt(this.e, this.n);
}
// Return the PKCS#1 RSA encryption of "text" as an even-length hex string
pidCrypt.RSA.prototype.encryptRaw = function(text) {
var m = pkcs1pad2(text,(this.n.bitLength()+7)>>3);
if(m == null) return null;
var c = this.doPublic(m);
if(c == null) return null;
var h = c.toString(16);
if((h.length & 1) == 0) return h; else return "0" + h;
}
pidCrypt.RSA.prototype.encrypt = function(text) {
//base64 coding for supporting 8bit chars
// PAY-7219: In order to support 16-bit characters, set optional parameter 'utf8encode' to 'true'
// then it will encode Unicode string into UTF-8. On the server side, we always decode string as UTF-8 already.
text = pidCryptUtil.encodeBase64(text, true);
return this.encryptRaw(text)
}
// Return the PKCS#1 RSA decryption of "ctext".
// "ctext" is an even-length hex string and the output is a plain string.
pidCrypt.RSA.prototype.decryptRaw = function(ctext) {
// alert('N='+this.n+'\nE='+this.e+'\nD='+this.d+'\nP='+this.p+'\nQ='+this.q+'\nDP='+this.dmp1+'\nDQ='+this.dmq1+'\nC='+this.coeff);
var c = parseBigInt(ctext, 16);
var m = this.doPrivate(c);
if(m == null) return null;
return pkcs1unpad2(m, (this.n.bitLength()+7)>>3)
}
pidCrypt.RSA.prototype.decrypt = function(ctext) {
var str = this.decryptRaw(ctext)
//base64 coding for supporting 8bit chars
// According to PAY-7219, set optional parameter 'utf8encode' to 'true'
// to properly decode multi-bytes character.
str = (str) ? pidCryptUtil.decodeBase64(str, true) : "";
return str;
}
/*
// Return the PKCS#1 RSA encryption of "text" as a Base64-encoded string
pidCrypt.RSA.prototype.b64_encrypt = function(text) {
var h = this.encrypt(text);
if(h) return hex2b64(h); else return null;
}
*/
// Set the private key fields N, e, and d from hex strings
pidCrypt.RSA.prototype.setPrivate = function(N,E,D,radix) {
if (typeof(radix) == 'undefined') radix = 16;
if(N != null && E != null && N.length > 0 && E.length > 0) {
this.n = parseBigInt(N,radix);
this.e = parseInt(E,radix);
this.d = parseBigInt(D,radix);
}
else
alert("Invalid RSA private key");
}
// Set the private key fields N, e, d and CRT params from hex strings
pidCrypt.RSA.prototype.setPrivateEx = function(N,E,D,P,Q,DP,DQ,C,radix) {
if (typeof(radix) == 'undefined') radix = 16;
if(N != null && E != null && N.length > 0 && E.length > 0) {
this.n = parseBigInt(N,radix);//modulus
this.e = parseInt(E,radix);//publicExponent
this.d = parseBigInt(D,radix);//privateExponent
this.p = parseBigInt(P,radix);//prime1
this.q = parseBigInt(Q,radix);//prime2
this.dmp1 = parseBigInt(DP,radix);//exponent1
this.dmq1 = parseBigInt(DQ,radix);//exponent2
this.coeff = parseBigInt(C,radix);//coefficient
}
else
alert("Invalid RSA private key");
// alert('N='+this.n+'\nE='+this.e+'\nD='+this.d+'\nP='+this.p+'\nQ='+this.q+'\nDP='+this.dmp1+'\nDQ='+this.dmq1+'\nC='+this.coeff);
}
// Generate a new random private key B bits long, using public expt E
pidCrypt.RSA.prototype.generate = function(B,E) {
var rng = new SecureRandom();
var qs = B>>1;
this.e = parseInt(E,16);
var ee = new BigInteger(E,16);
for(;;) {
for(;;) {
this.p = new BigInteger(B-qs,1,rng);
if(this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.p.isProbablePrime(10)) break;
}
for(;;) {
this.q = new BigInteger(qs,1,rng);
if(this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.q.isProbablePrime(10)) break;
}
if(this.p.compareTo(this.q) <= 0) {
var t = this.p;
this.p = this.q;
this.q = t;
}
var p1 = this.p.subtract(BigInteger.ONE);
var q1 = this.q.subtract(BigInteger.ONE);
var phi = p1.multiply(q1);
if(phi.gcd(ee).compareTo(BigInteger.ONE) == 0) {
this.n = this.p.multiply(this.q);
this.d = ee.modInverse(phi);
this.dmp1 = this.d.mod(p1);
this.dmq1 = this.d.mod(q1);
this.coeff = this.q.modInverse(this.p);
break;
}
}
}
//pidCrypt extensions start
//
pidCrypt.RSA.prototype.getASNData = function(tree) {
var params = {};
var data = [];
var p=0;
if(tree.value && tree.type == 'INTEGER')
data[p++] = tree.value;
if(tree.sub)
for(var i=0;i