It appears that the "key" is the entire line of file1. If so, then this is a pretty easy task.

Here is an example:

use Modern::Perl;

my %keys;

open my $file1, '<', 'filename1.txt' or die "Can't open file 1: $!";
open my $file2, '<', 'filename2.txt' or die "Can't open file 2: $!";

#read in the first file.
while (<$file1>)
{
    chomp;             #remove newline.
    $keys{$_}++;    #Add the key to your hash
}

#find keys in the second file.
while (<$file2>)
{
    foreach my $key (keys %keys)
    {
        say "$key matches" if /\b\Q$key\E\b/;
    }     
}
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Regex Notes: \b matches a word boundary. This is because you presumably wouldn't want "John Smith" to match "John Smithfield". \Q...\E is the quote literal modifier. If your key contains characters with a special meaning in regexes (such as the dot in "Mr. Smith") you want to match only the literal characters.

Yes, you do end up needing a nested loop...that is intrinsic to the nature of your task.