Initial data commit

Task/Elliptic-Curve-Digital-Signature-Algorithm/Raku/elliptic-curve-digital-signature-algorithm.raku

@@ -0,0 +1,89 @@
+use Digest::SHA256::Native;
+
+# Following data taken from the C entry
+our (\A,\B,\P,\O,\Gx,\Gy) = (355, 671, 1073741789, 1073807281, 13693, 10088);
+
+#`{ Following data taken from the Julia entry; 256-bit; tested
+our (\A,\B,\P,\O,\Gx,\Gy) = (0, 7, # https://en.bitcoin.it/wiki/Secp256k1
+0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F,
+0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,
+0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
+0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8); # }
+
+role Horizon { method gist { 'EC Point at horizon' } }
+
+class Point {             # modified from the Elliptic_curve_arithmetic entry
+   has ($.x, $.y);        # handle modular arithmetic only
+   multi method new( \x, \y ) { self.bless(:x, :y) }
+   method gist { "EC Point at x=$.x, y=$.y" }
+   method isOn { modP(B + $.x * modP(A+$.x²)) == modP($.y²) }
+   sub modP ($a is copy) { ( $a %= P ) < 0 ?? ($a += P) !! $a }
+}
+
+multi infix:<⊞>(Point \p, Point \q) {)
+   my \λ = $; # slope
+   if p.x ~~ q.x and p.y ~~ q.y {.
+      return Horizon if p.y == 0 ;
+      λ = (3*p.x²+ A) * mult_inv(2*p.y, :modulo(P))
+   } else {
+      λ = (p.y - q.y) * mult_inv(p.x - q.x, :modulo(P)).
+   }
+   my \xr = (λ²- p.x - q.x);.
+   my \yr = (λ*(p.x - xr) - p.y);
+   return Point.bless: x =>  xr % P, y => yr % P
+}
+
+multi infix:<⊠>(Int \n, Point \p) {
+   return 0                if n == 0 ;
+   return p                if n == 1 ;
+   return p ⊞ ((n-1) ⊠ p ) if n % 2 == 1 ;
+   return ( n div 2 ) ⊠ ( p ⊞ p )
+}
+
+sub mult_inv($n, :$modulo) { # rosettacode.org/wiki/Modular_inverse#Raku
+   my ($c, $d, $uc, $vd, $vc, $ud, $q) = $n % $modulo, $modulo, 1, 1, 0, 0, 0;
+   while $c != 0 {
+      ($q, $c, $d) = ($d div $c, $d % $c, $c);
+      ($uc, $vc, $ud, $vd) = ($ud - $q*$uc, $vd - $q*$vc, $uc, $vc);
+   }
+   return $ud % $modulo;
+}
+
+class Signature {
+
+   has ($.n, Point $.G); # Order and Generator point
+
+   method generate_signature(Int \private_key, Str \msg) {
+      my \z = :16(sha256-hex msg) % $.n; # self ref: Blob.list.fmt("%02X",'')
+      loop ( my $k = my $s = my $r = 0 ; $s == 0 ; ) {
+         loop ( $r = $s = 0 ; $r == 0 ; ) {
+            $r = (( $k = (1..^$.n).roll ) ⊠ $.G).x % $.n;
+         }
+         $s = ((z + $r*private_key) * mult_inv $k, :modulo($.n)) % $.n;
+      }
+      return $r, $s, private_key ⊠ $.G ;
+   }
+
+   method verify_signature(\msg, \r, \s, \public_key) {
+      my \z = :16(sha256-hex msg) % $.n;
+      my \w = mult_inv s, :modulo($.n);
+      my (\u1,\u2) = (z*w, r*w).map: { $_ % $.n }
+      my \p = (u1 ⊠ $.G ) ⊞ (u2 ⊠ public_key);
+      return (p.x % $.n) == (r % $.n)
+   }
+}
+
+print "The Curve E is        : ";
+"𝑦² = 𝑥³ + %s 𝑥 + %s (mod %s) \n".printf(A,B,P);
+"with Generator G at   : (%s,%s)\n".printf(Gx,Gy);
+my $ec = Signature.new: n => O, G => Point.new: x => Gx, y => Gy ;
+say "Order(G, E) is        : ", O;
+say "Is G  ∈ E ?           : ", $ec.G.isOn;
+say "Message               : ", my \message = "Show me the monKey";
+say "The private key dA is : ", my \dA = (1..^O).roll;
+my ($r, $s, \Qa) = $ec.generate_signature(dA, message);
+say "The public  key Qa is : ", Qa;;
+say "Is Qa ∈ E ?           : ", Qa.isOn;.
+say "Is signature valid?   : ", $ec.verify_signature(message, $r, $s, Qa);)
+say "Message (Tampered)    : ", my \altered = "Show me the money";
+say "Is signature valid?   : ", $ec.verify_signature(altered, $r, $s, Qa))