I wrote the code you need.

Some utility functions

sub read_bytes {
   my ($fh, $to_read) = @_;
   my $buf = '';
   while ($to_read) {
      my $bytes_read = read($fh, $buf, $to_read, length($buf));
      die("$!\n") if !defined($bytes_read);
      die("Unexpected end of file\n") if !$bytes_read;
      $to_read -= $bytes_read;
   }
   return $buf;
}

sub read_uint32 {
   my ($fh) = @_;
   return (unpack('N', read_bytes($fh, 4)));
}

sub read_str {
   my ($fh) = @_;
   my $length = read_uint32($fh);
   return read_bytes($fh, $length);
}

sub write_uint32 {
   my ($fh, $n) = @_;
   print $fh (pack('N', $n));
}

sub write_str {
   my ($fh, $str) = @_;
   print $fh (pack('N', length($str)), $str);
}
[download]

The line-by-line encrypter:

sub writeSubmissions {
   my ($cipher, $log_file, $str) = @_;

   open(my $FH_encrypted, '>>', $log_file)
      or die;
   binmode $FH_encrypted;
   flock $FH_encrypted, LOCK_EX;

   write_str($FH_encrypted, $cipher->encrypt($str));
}

my $key_file = 'key_file.txt';
my $act_log_file = "pem.enc";
my $pem_log_file = "act_encrypted.enc";

my $my_key = `openssl enc -bf-cbc -d -in \Q$key_file\E -k encrypt`;
my $cipher = Crypt::CBC->new({ key => $my_key, cipher => 'Rijndael' })
+;

writeSubmissions($cipher, ..., ...);
[download]

The line-by-line decrypter:

my $key_file = 'key_file.txt';
my $encrypted = '...';
my $decrypted = '...';

my $my_key = `openssl enc -bf-cbc -d -in \Q$key_file\E -k encrypt`;
my $cipher = Crypt::CBC->new({ key => $my_key, cipher => 'Rijndael' })
+;

open(my $FH_decrypted, '>', $decrypted)
   or die("Unable to create decrypted file \"$decrypted\": $!\n");
binmode $FH_decrypted;
flock $FH_decrypted, LOCK_EX;

open(my $FH_encrypted, '<', $encrypted)
   or die("Unable to open encrypted file \"$encrypted\": $!\n");
binmode $FH_encrypted;
flock $FH_encrypted, LOCK_SH;

while (!eof($FH_encrypted)) {
   print $FH_decrypted $cipher->decrypt(read_str($FH_encrypted));
}
[download]

Update: Fixed bugs mentioned in replies.
Update: Tested (minus the openssl bit). Fixed other bugs.

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