This is a solution to Advent of Code 2020 day 25, written in Raku.

https://adventofcode.com/2020/day/25

### Part One

What encryption key is the handshake trying to establish?

The first step of this solution finds the exponent `$loop-value`

for card and door by
brute-force search. Then we can rapidly calculate the encryption key from either public-key /
exponent pair using `expmod`

.

```
my Int ($card-public, $door-public) = '25-input.txt'.IO.lines>>.Int;
sub calc-loop-values(*@publics) {
my $wanted = SetHash.new(@publics);
my %loop-values = gather {
my $i = 1;
my $value = 1;
while +$wanted {
$value = ($value * 7) % 20201227;
if $wanted{$value} {
take $value => $i;
$wanted.unset($value);
}
$i++;
}
}
%loop-values;
}
my %loop-values = calc-loop-values($card-public, $door-public);
say %loop-values;
say expmod($card-public, %loop-values{$door-public}, 20201227);
say expmod($door-public, %loop-values{$card-public}, 20201227);
```

{16915772 => 4618530, 18447943 => 6662323} 6011069 6011069