Data update
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Ingy döt Net
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858 changed files with 20572 additions and 2082 deletions
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@ -1,89 +1,101 @@
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use Digest::SHA256::Native;
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module EC {
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use FiniteField;
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# Following data taken from the C entry
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our (\A,\B,\P,\O,\Gx,\Gy) = (355, 671, 1073741789, 1073807281, 13693, 10088);
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our class Point {
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has ($.x, $.y);
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submethod TWEAK { fail unless $!y**2 == $!x**3 + $*a*$!x + $*b }
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multi method gist(::?CLASS:U:) { "Point at Horizon" }
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multi method new($x, $y) { samewith :$x, :$y }
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}
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multi infix:<==>(Point:D $A, Point:D $B) is export { $A.x == $B.x and $A.y == $B.y }
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#`{ Following data taken from the Julia entry; 256-bit; tested
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our (\A,\B,\P,\O,\Gx,\Gy) = (0, 7, # https://en.bitcoin.it/wiki/Secp256k1
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0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F,
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0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,
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0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
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0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8); # }
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multi prefix:<->(Point $P) returns Point is export { Point.new: $P.x, -$P.y }
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multi infix:<+>(Point $A, Point:U) is export { $A }
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multi infix:<+>(Point:U, Point $B) is export { $B }
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multi infix:<+>(Point:D $A, Point:D $B) returns Point is export {
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my $λ;
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if $A.x == $B.x and $A.y == -$B.y { return Point }
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elsif $A == $B {
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return Point if $A.y == 0;
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$λ = (3*$A.x² + $*a) / (2*$A.y);
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}
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else { $λ = ($A.y - $B.y) / ($A.x - $B.x); }
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role Horizon { method gist { 'EC Point at horizon' } }
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class Point { # modified from the Elliptic_curve_arithmetic entry
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has ($.x, $.y); # handle modular arithmetic only
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multi method new( \x, \y ) { self.bless(:x, :y) }
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method gist { "EC Point at x=$.x, y=$.y" }
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method isOn { modP(B + $.x * modP(A+$.x²)) == modP($.y²) }
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sub modP ($a is copy) { ( $a %= P ) < 0 ?? ($a += P) !! $a }
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given $λ**2 - $A.x - $B.x {
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return Point.new: $_, $λ*($A.x - $_) - $A.y;
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}
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}
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multi infix:<*>(0, Point ) is export { Point }
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multi infix:<*>(1, Point $p) is export { $p }
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multi infix:<*>(2, Point:D $p) is export { $p + $p }
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multi infix:<*>(Int $n, Point $p) is export { 2*(($n div 2)*$p) + ($n mod 2)*$p }
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}
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multi infix:<⊞>(Point \p, Point \q) {)
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my \λ = $; # slope
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if p.x ~~ q.x and p.y ~~ q.y {.
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return Horizon if p.y == 0 ;
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λ = (3*p.x²+ A) * mult_inv(2*p.y, :modulo(P))
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} else {
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λ = (p.y - q.y) * mult_inv(p.x - q.x, :modulo(P)).
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}
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my \xr = (λ²- p.x - q.x);.
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my \yr = (λ*(p.x - xr) - p.y);
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return Point.bless: x => xr % P, y => yr % P
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}
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import EC;
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multi infix:<⊠>(Int \n, Point \p) {
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return 0 if n == 0 ;
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return p if n == 1 ;
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return p ⊞ ((n-1) ⊠ p ) if n % 2 == 1 ;
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return ( n div 2 ) ⊠ ( p ⊞ p )
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}
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sub mult_inv($n, :$modulo) { # rosettacode.org/wiki/Modular_inverse#Raku
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my ($c, $d, $uc, $vd, $vc, $ud, $q) = $n % $modulo, $modulo, 1, 1, 0, 0, 0;
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while $c != 0 {
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($q, $c, $d) = ($d div $c, $d % $c, $c);
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($uc, $vc, $ud, $vd) = ($ud - $q*$uc, $vd - $q*$vc, $uc, $vc);
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}
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return $ud % $modulo;
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}
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class Signature {
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has ($.n, Point $.G); # Order and Generator point
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method generate_signature(Int \private_key, Str \msg) {
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my \z = :16(sha256-hex msg) % $.n; # self ref: Blob.list.fmt("%02X",'')
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loop ( my $k = my $s = my $r = 0 ; $s == 0 ; ) {
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loop ( $r = $s = 0 ; $r == 0 ; ) {
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$r = (( $k = (1..^$.n).roll ) ⊠ $.G).x % $.n;
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}
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$s = ((z + $r*private_key) * mult_inv $k, :modulo($.n)) % $.n;
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module ECDSA {
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use Digest::SHA256::Native;
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our class Signature {
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has UInt ($.c, $.d);
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multi method new(Str $message, UInt :$private-key) {
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my $z = :16(sha256-hex $message) % $*n;
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loop (my $k = my $s = my $r = 0; $r == 0; ) {
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loop ( $r = $s = 0 ; $r == 0 ; ) {
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$r = (( $k = (1..^$*n).roll ) * $*G).x % $*n;
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}
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{
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use FiniteField; my $*modulus = $*n;
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$s = ($z + $r*$private-key) / $k;
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}
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}
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return $r, $s, private_key ⊠ $.G ;
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}
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method verify_signature(\msg, \r, \s, \public_key) {
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my \z = :16(sha256-hex msg) % $.n;
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my \w = mult_inv s, :modulo($.n);
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my (\u1,\u2) = (z*w, r*w).map: { $_ % $.n }
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my \p = (u1 ⊠ $.G ) ⊞ (u2 ⊠ public_key);
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return (p.x % $.n) == (r % $.n)
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}
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samewith c => $r, d => $s;
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}
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multi method verify(Str $message, EC::Point :$public-key) {
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my $z = :16(sha256-hex $message) % $*n;
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my ($u1, $u2);
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{
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use FiniteField;
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my $*modulus = $*n;
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my $w = 1/$!d;
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($u1, $u2) = $z*$w, $!c*$w;
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}
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my $p = ($u1 * $*G) + ($u2 * $public-key);
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die unless ($p.x mod $*n) == ($!c mod $*n);
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}
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}
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}
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print "The Curve E is : ";
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"𝑦² = 𝑥³ + %s 𝑥 + %s (mod %s) \n".printf(A,B,P);
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"with Generator G at : (%s,%s)\n".printf(Gx,Gy);
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my $ec = Signature.new: n => O, G => Point.new: x => Gx, y => Gy ;
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say "Order(G, E) is : ", O;
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say "Is G ∈ E ? : ", $ec.G.isOn;
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say "Message : ", my \message = "Show me the monKey";
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say "The private key dA is : ", my \dA = (1..^O).roll;
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my ($r, $s, \Qa) = $ec.generate_signature(dA, message);
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say "The public key Qa is : ", Qa;;
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say "Is Qa ∈ E ? : ", Qa.isOn;.
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say "Is signature valid? : ", $ec.verify_signature(message, $r, $s, Qa);)
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say "Message (Tampered) : ", my \altered = "Show me the money";
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say "Is signature valid? : ", $ec.verify_signature(altered, $r, $s, Qa))
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my ($*a, $*b) = 355, 671;
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my $*modulus = my $*p = 1073741789;
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my $*G = EC::Point.new: 13693, 10088;
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my $*n = 1073807281;
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die "G is not of order n" if $*n*$*G;
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my $private-key = ^$*n .pick;
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my $public-key = $private-key*$*G;
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my $message = "Show me the monKey";
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my $signature = ECDSA::Signature.new: $message, :$private-key;
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printf "The curve E is : 𝑦² = 𝑥³ + %s 𝑥 + %s (mod %s)\n", $*a, $*b, $*p;
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printf "with generator G at : (%s, %s)\n", $*G.x, $*G.y;
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printf "G's order is : %d\n", $*n;
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printf "The private key is : %d\n", $private-key;
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printf "The public key is at : (%s, %s)\n", $public-key.x, $public-key.y;
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printf "The message is : %s\n", $message;
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printf "The signature is : (%s, %s)\n", $signature.c, $signature.d;
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{
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use Test;
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lives-ok {
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$signature.verify: $message, :$public-key;
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}, "good signature for <$message>";
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my $altered = $message.subst(/monKey/, "money");
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dies-ok {
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$signature.verify: $altered, :$public-key
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}, "wrong signature for <$altered>";
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}
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