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use Math::BigInt only => 'GMP';
use Digest::Keccak qw(keccak_256);
my $p = Math::BigInt->new(2)->bpow(255)->bsub(19); #F_p
my $l = Math::BigInt->new(2)->bpow(252)->badd('27742317777372353535851937790883648493');
#my $d = Math::BigInt->new(486662); #motgomery: y^2 = x^3 + 486662x^2 + x
my $d = Math::BigInt->new(-121665)->bmul(minv(121666))->bmod($p); #twisted edwards: -x^2 +y^2 = 1 + d*x^2*y^2
my $x0 = Math::BigInt->new('15112221349535400772501151409588531511454012693041857206046113283949847762202');
my $y0 = Math::BigInt->new('46316835694926478169428394003475163141307993866256225615783033603165251855960'); #y0 = 4/5
my $m = Math::BigInt->new('7237005577332262213973186563042994240829374041602535252466099000494570602493'); #p = 8m+5
my $ps = $p->copy()->bdec->bdiv(4);
my $pl = $p->copy()->bdec->bdiv(2);
my $ii = Math::BigInt->new(2)->bmodpow($ps,$p); #sqrt(-1)
sub ec_rec {
my $y = Math::BigInt->new($_[0]);
my $xx = $y->copy()->bpow(2)->bdec()->bmul(minv($y->copy()->bpow(2)->bmul($d)->binc))->bmod($p);
return 0 if !($xx->copy()->bmodpow($pl,$p)->binc->bmod($p));
my $p2 = $p->copy()->badd(3)->bdiv(8);
my $x = $xx->copy()->bmodpow($p2, $p);
if ($x->copy()->bpow(2)->bsub($xx)->bmod($p)) {$x->bmul($ii)->bmod($p)}
if ($x->is_odd) {$x = $p->copy()->bsub($x)};
return $x;
}
sub h2i {
return Math::BigInt->new('0x'.(unpack 'H*', (reverse pack 'H*', shift)));;
}
sub i2h {
my $t = substr(Math::BigInt->new(shift)->as_hex(),2,64);
if (length($t)%2 == 1) {$t = '0'.$t}
return unpack 'H*', (reverse pack 'H*', $t);
}
sub random {
return keccak_256(rand(2**20));
#return keccak_256(3); #I swear that's random!
}
sub ec_pack {
my $x = Math::BigInt->new($_[0]);
my $y = Math::BigInt->new($_[1]);
my $or = Math::BigInt->new(2)->bpow(255);
$y |= $or if ($x->is_odd());
return unpack 'H*', (reverse pack 'H*', substr($y->as_hex(),2,64));
}
sub ec_unpack {
my $y = Math::BigInt->new(h2i(shift));
my $b = $y >> 255;
my $and = Math::BigInt->new(2)->bpow(255)->bdec();
$y &= $and;
my $x = ec_rec($y);
return (0,0) if $x==0;
($b==0) || ($x = $p->copy()->bsub($x));
return ($x,$y);
}
sub minv {
my $x = Math::BigInt->new(shift);
$x->bmodpow($p-2,$p);
return $x;
}
sub ec_doub {
my $x = Math::BigInt->new($_[0]);
my $y = Math::BigInt->new($_[1]);
#$t = $x->copy()->bpow(2)->bmul(3)->badd($x->copy()->bmul($d)->bmul(2))->binc()->bmul(minv($y->copy()->bmul(2))); #montgomery
#$x2 = $t->copy()->bpow(2)->bsub($d)->bsub($x)->bsub($x)->bmod($p); #montgomery
#$y2 = $x->copy()->bmul(2)->badd($x)->badd($d)->bmul($t)->bsub($t->copy()->bpow(3))->bsub($y)->bmod($p); #montgomery
$t = $x->copy()->bmul($x)->bmul($y)->bmul($y)->bmul($d)->bmod($p);
$x3 = $x->copy()->bmul($y)->bmul(2)->bmul(minv($t+1))->bmod($p);
$y3 = $y->copy()->bpow(2)->badd($x->copy()->bpow(2))->bmul(minv(1-$t))->bmod($p);
return ($x3,$y3);
}
sub ec_add {
my $x1 = Math::BigInt->new($_[0]);
my $y1 = Math::BigInt->new($_[1]);
my $x2 = Math::BigInt->new($_[2]);
my $y2 = Math::BigInt->new($_[3]);
#$t = $y2->copy()->bsub($y1)->bmul(minv($x2->copy()->bsub($x1)));
#$x3 = $t->copy()->bpow(2)->bsub($d)->bsub($x1)->bsub($x2)->bmod($p);
#$y3 = $x1->copy()->bmul(2)->badd($x2)->badd($d)->bmul($t)->bsub($t->copy()->bpow(3))->bsub($y1)->bmod($p);
$t = $x1->copy->bmul($x2)->bmul($y1)->bmul($y2)->bmul($d)->bmod($p);
$x3 = $x1->copy()->bmul($y2)->badd($y1->copy()->bmul($x2))->bmul(minv($t+1))->bmod($p);
$y3 = $y1->copy()->bmul($y2)->badd($x1->copy()->bmul($x2))->bmul(minv(1-$t))->bmod($p);
return ($x3,$y3);
}
sub ec_mul {
my $n = Math::BigInt->new($_[0]);
my $x = Math::BigInt->new($_[1]);
my $y = Math::BigInt->new($_[2]);
if ($n->is_one()) {
return ($x,$y);
last;
}
elsif ($n->is_even()) {
$n->bdiv(2);
return ec_mul($n,&ec_doub($x,$y));
}
else {
$n->bdec()->bdiv(2);
return ec_add($x,$y,ec_mul($n,&ec_doub($x,$y)));
}
}
sub pkeygen {
my $key = Math::BigInt->new(h2i(shift))->bmod($l);
return ec_pack(ec_mul($key,$x0,$y0));
}
sub ec_hash {
my $h = pack 'H*', shift;
my $h = Math::BigInt->new('0x'.(unpack 'H*', reverse keccak_256($h)));
my ($x,$y) = (0,0);
while ($x == 0) {
($x,$y) = ec_unpack(i2h($h));
$h->binc();
}
return ec_mul(8,$x,$y);
}
sub im_gen {
my ($x,$y) = ec_hash(shift);
my $k = Math::BigInt->new(h2i(shift))->bmod($l);
return ec_pack(ec_mul($k,$x,$y));
}
sub sign {
my ($m,$sec_key) = @_;
my $sec_key = Math::BigInt->new(h2i($sec_key));
my ($x,$y) = ec_mul($sec_key,$x0,$y0);
my $k = Math::BigInt->new('0x'.(unpack 'H*', random()))->bmod($l);
#my $k = Math::BigInt->new('5267557024171956683337957876581522196748200715787296882078421399301151717969');
my $e = unpack 'H*', keccak_256($m.(pack 'H*', ec_pack(ec_mul($k,$x0,$y0))));
my $s = i2h(Math::BigInt->new(h2i($e))->bmul($sec_key)->bneg()->badd($k)->bmod($l));
$e = i2h(Math::BigInt->new(h2i($e))->bmod($l));
return ($s,$e);
}
sub check_s {
my ($m,$pt,$s1,$e1) = @_;
my ($x,$y) = ec_unpack($pt);
my $s = Math::BigInt->new(h2i($s1))->bmod($l);
my $e = Math::BigInt->new(h2i($e1))->bmod($l);
my ($x1,$y1) = ec_add(ec_mul($s,$x0,$y0),ec_mul($e,$x,$y));
$m = $m.(pack 'H*', ec_pack($x1,$y1));
my $ev = Math::BigInt->new(h2i(unpack 'H*', keccak_256($m)))->bmod($l);
return !$ev->bcmp($e);
}
sub r_sign {
my ($m,$image,$sec_key,$index,@pkeys) = @_;
my ($ix,$iy) = ec_unpack($image);
my $n = @pkeys;
my $data = $m;
my $w = $a = $b = $hx = $hy = $px = $py = 0;
my @zc = ();
my $sum = Math::BigInt->new();
#print "begin signing ($n keys)\n";
for $i (0..$n-1) {
($hx, $hy) = ec_hash(@pkeys[$i]);
($px,$py) = ec_unpack(@pkeys[$i]);
if ($i == $index) {
$w = Math::BigInt->new('0x'.(unpack 'H*', random()))->bmod($l);
$a = pack 'H*', ec_pack(ec_mul($w,$x0,$y0));
$b = pack 'H*', ec_pack(ec_mul($w,$hx,$hy));
push @zc,0,0;
}
else {
$z = Math::BigInt->new('0x'.(unpack 'H*', random()))->bmod($l);
$c = Math::BigInt->new('0x'.(unpack 'H*', random()))->bmod($l);
$sum->badd($c);
$a = pack 'H*', ec_pack(ec_add(ec_mul($z,$x0,$y0),ec_mul($c,$px,$py)));
$b = pack 'H*', ec_pack(ec_add(ec_mul($z,$hx,$hy),ec_mul($c,$ix,$iy)));
push @zc,i2h($z),i2h($c);
}
$data = $data.$a.$b;
#print "key number $i done\n";
}
#print "generating ringsig..\n";
my $h = unpack 'H*', keccak_256($data);
my $cy = Math::BigInt->new(h2i($h))->bsub($sum)->bmod($l);
my $zy = $cy->copy()->bmul(h2i($sec_key))->bneg()->badd($w)->bmod($l);
@zc[2*$index] = i2h($zy);
@zc[2*$index+1] = i2h($cy);
return @zc;
}
sub r_check_s {
my ($m,$image,@zc) = @_;
my $n = @zc/3;
for $j (0..$n-1) {
@pkeys[$j] = shift @zc;
}
my $data = $m;
my ($ix,$iy) = ec_unpack($image);
my $a = $b = $hx = $hy = $px = $py = $z = $c = 0;
my $sum = Math::BigInt->new();
#print "\nBegin checking ($n keys)\n";
for $i (0..$n-1) {
$z = Math::BigInt->new(h2i(shift @zc))->bmod($l);
$c = Math::BigInt->new(h2i(shift @zc))->bmod($l);
$sum->badd($c)->bmod($l);
($px,$py) = ec_unpack(@pkeys[$i]);
$a = pack 'H*', ec_pack(ec_add(ec_mul($z,$x0,$y0),ec_mul($c,$px,$py)));
($hx, $hy) = ec_hash(@pkeys[$i]);
$b = pack 'H*', ec_pack(ec_add(ec_mul($z,$hx,$hy),ec_mul($c,$ix,$iy)));
$data = $data.$a.$b;
#print "key number $i done\n";
}
my $h = Math::BigInt->new(h2i(unpack 'H*', keccak_256($data)))->bmod($l);
return !$h->bcmp($sum);
}
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