Elliptic Curve Digital Signature Algorithm: Difference between revisions

Content added Content deleted
(→‎{{header|Perl 6}}: Update: use another lib for SHA; try bigger data set ; borrow point on curve check routine from reference entries ; more verbose output ; get rid of pack , etc)
m (→‎{{header|Perl 6}}: Thanks to Thundergnat for the advice ; use the correct lib ; remove unnecessary int/str round trip ; echo the Julia entry by showing a failure and suppress naughty hyper)
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Reference: Many routines are translated from this [https://github.com/sblackstone/toy-ecdsa Ruby repository], by Stephen Blackstone. The rest are taken here and there from RC.
Reference: Many routines are translated from this [https://github.com/sblackstone/toy-ecdsa Ruby repository], by Stephen Blackstone. The rest are taken here and there from RC.
<lang perl6>#!/usr/bin/env perl6
<lang perl6>#!/usr/bin/env perl6

use Digest::SHA;
use Digest::SHA256::Native;


# Following data taken from the C entry
# Following data taken from the C entry
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#`{ Following data taken from the Julia entry; 256-bit; tested
#`{ 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
our (\A,\B,\P,\O,\Gx,\Gy) = (0, 7, # https://en.bitcoin.it/wiki/Secp256k1
:10("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F"),
0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F,
:10("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141"),
0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,
:10("0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798"),
0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
:10("0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8")); # }
0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8); # }


role Horizon { method gist { 'EC Point at horizon' } }
role Horizon { method gist { 'EC Point at horizon' } }
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method generate_signature(Int \private_key, Str \msg) {
method generate_signature(Int \private_key, Str \msg) {
my \z = :16((sha256 msg).list>>.&{"%02s".sprintf(.base(16))}.join) % $.n;
my \z = :16(sha256-hex msg) % $.n; # self ref: Blob.list.fmt("%02X",'')
loop (my $k = my $s = my $r = 0 ; $s == 0 ; ) {
loop ( my $k = my $s = my $r = 0 ; $s == 0 ; ) {
loop ($r = $s = 0 ; $r == 0 ; ) {
loop ( $r = $s = 0 ; $r == 0 ; ) {
$r = (( $k = (1..^$.n).roll ) ⊠ $.G).x % $.n;
$r = (( $k = (1..^$.n).roll ) ⊠ $.G).x % $.n;
}
}
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method verify_signature(\msg, \r, \s, \public_key) {
method verify_signature(\msg, \r, \s, \public_key) {
my \z = :16((sha256 msg).list>>.&{"%02s".sprintf(.base(16))}.join) % $.n;
my \z = :16(sha256-hex msg) % $.n;
my \w = mult_inv s, :modulo($.n);
my \w = mult_inv s, :modulo($.n);
my (\u1,\u2) = (z*w, r*w)>>.&{ $_ % $.n }
my (\u1,\u2) = (z*w, r*w).map: { $_ % $.n }
my \p = (u1 ⊠ $.G ) ⊞ (u2 ⊠ public_key);
my \p = (u1 ⊠ $.G ) ⊞ (u2 ⊠ public_key);
return (p.x % $.n) == (r % $.n)
return (p.x % $.n) == (r % $.n)
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say "The public key Qa is : ", Qa;
say "The public key Qa is : ", Qa;
say "Is Qa ∈ E ? : ", Qa.isOn;
say "Is Qa ∈ E ? : ", Qa.isOn;
say "Is signature valid? : ", $ec.verify_signature(message, $r, $s, Qa)
say "Is signature valid? : ", $ec.verify_signature(message, $r, $s, Qa);
say "Message (Tampered) : ", my \altered = "Show me the money";
</lang>
say "Is signature valid? : ", $ec.verify_signature(altered, $r, $s, Qa)</lang>
{{out}}
{{out}}
<pre>The Curve E is : 𝑦² = 𝑥³ + 355 𝑥 + 671 (mod 1073741789)
<pre>The Curve E is : 𝑦² = 𝑥³ + 355 𝑥 + 671 (mod 1073741789)
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Is G ∈ E ? : True
Is G ∈ E ? : True
Message : Show me the monKey
Message : Show me the monKey
The private key dA is : 31462688
The private key dA is : 384652035
The public key Qa is : EC Point at x=105863728, y=654043071
The public key Qa is : EC Point at x=919494857, y=18030536
Is Qa ∈ E ? : True
Is Qa ∈ E ? : True
Is signature valid? : True
Is signature valid? : True
Message (Tampered) : Show me the money
Is signature valid? : False
</pre>
</pre>


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