Challenge 1

Write a script to generate first 10 strong and weak prime numbers.

Which is determined by:

Strong Prime number p(n) when p(n) > [ p(n-1) + p(n+1) ] / 2

Weak Prime number p(n) when p(n) < [ p(n-1) + p(n+1) ] / 2

This led me to a question. 2 is p(1), so how do we work that into this? p(n-1) is not defined, because 2 is the lowest prime. Or is it? Please tell men.

#!/usr/bin/env perl

use strict;
use warnings;
use feature qw{ postderef say signatures state };
no warnings qw{ experimental::postderef experimental::signatures };

# Write a script to generate first 10 strong and weak prime numbers.

# https://en.wikipedia.org/wiki/Strong_prime
#  (which contains a list of strong primes to ensure things are correct)

my @primes;
my @strong;
my @weak;

# create list of primes to judge strong, weak or balanced
while ( @strong < 10 && @weak < 10 ) {
    state $c += 1;
    if ( is_prime($c) ) { push @primes, $c }
    last if scalar @primes > 100;
}

for my $n ( 1 .. @primes ) {
    my $swb = is_strong($n);
    my $o   = $primes[$n];
    push @strong, $o if $swb == 1;
    push @weak,   $o if $swb == -1;
    last if @weak > 10 && @strong > 10;
}
say 'strong:  ' . join ", ",  @strong[0..9];
say 'weak:    ' . join ", ",  @weak[0..9];
exit;

# 1 if strong
# -1 if weak
# 0 if balanced
sub is_strong ( $n ) {
    my $o = $primes[$n];
    return 3 if $n <= 0;    # no n-1 -- look up this special case
    return 4
        if !$primes[ $n + 1 ];  # no n+1 -- we should be done well before then
    my $p = ( $primes[ $n - 1 ] + $primes[ $n + 1 ] ) / 2;
    return 1  if $o > $p;
    return -1 if $o < $p;
    return 0;
}

# this one again
sub is_prime ( $n ) {
    my @factors = factor($n);
    return scalar @factors == 1 ? 1 : 0;
}

# this has a slight modification, going only to sqrt $n, because
# there can't be a factor above that. Duh.
sub factor ( $n ) {
    my @factors;
    for my $i ( 1 .. sqrt $n ) {
        push @factors, $i if $n % $i == 0;
    }
    return @factors;
}

strong:  11, 17, 29, 37, 41, 59, 67, 71, 79, 97
weak:    3, 7, 13, 19, 23, 31, 43, 47, 61, 73

Unless 2 is a weak prime. I believe in my code, but I don’t know if it fully conforms with the mathematical definition.

Challenge 2

Write a script to implement Vigenère cipher. The script should be able encode and decode. Checkout wiki page for more information.

Crypto! And old-school crypto at that. There are two kinds of cryptography in this world: cryptography that will stop your kid sister from reading your files, and cryptography that will stop major governments from reading your files. This challenge is about the former.

The core of this sort of cypher is this box:

   0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
   0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
00 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
01 B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
02 C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
03 D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
04 E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
05 F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
06 G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
07 H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
08 I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
09 J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
10 K L M N O P Q R S T U V W X Y Z A B C D E F G H I J
11 L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
12 M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
13 N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
14 O P Q R S T U V W X Y Z A B C D E F G H I J K L M N
15 P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
16 Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
17 R S T U V W X Y Z A B C D E F G H I J K L M N O P Q
18 S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
19 T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
20 U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
21 V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
22 W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
23 X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
24 Y Z A B C D E F G H I J K L M N O P Q R S T U V W X
25 Z A B C D E F G H I J K L M N O P Q R S T U V W X Y

Assume the keyword is ‘NEXT’ and the cleartext is ‘PERLCHALLENGE’, you start with finding N is letter 13 and P is letter 15, finding that row 13, column 15 gives us C (and actually, row 15, column 13 gives us the same), so our cyphertext starts with C.

To reverse it, we find which column gives us cyphertext C when row is 13, which is 15, which is P.

#!/usr/bin/env perl

use strict;
use warnings;
use feature qw{ postderef say signatures state fc };
no warnings qw{ experimental::postderef experimental::signatures };

my $keyword   = 'ATTACKATDAWN';
my $cleartext = <<'END';
Write a script to implement Vigenere cipher.
The script should be able encode and decode.
END

# the point ISN'T to show off Getopt or File I/O techniques
# so I'm going way simple here.
$keyword   = $ARGV[0] ? $ARGV[0] : $keyword;
$cleartext = $ARGV[1] ? $ARGV[1] : $cleartext;

$keyword =~ tr/a-z/A-Z/;
$keyword =~ s/\W//g;
$cleartext =~ tr/a-z/A-Z/;    # or uc $cleartext. TMTOWTDI
$cleartext =~ s/\W//g;        # text that isn't alpha isn't encrypted
                              # and can give the game away.

my $cyphertext = encode_vigenere( $keyword, $cleartext );
my $decrypt = decode_vigenere( $keyword, $cyphertext );
say <<"END";
    CLEAR:
        $cleartext
    CYPHER:
        $cyphertext
    DECRYPT:
        $decrypt
END
exit;

sub encode_vigenere ( $keyword, $cleartext ) {
    my @keyword = split m{}, $keyword;
    my @base    = make_core_cypher();
    my @alpha   = 'A' .. 'Z';
    my %alpha   = map { $alpha[$_] => $_ } 0 .. 25;
    my @cypher;
    for my $clear ( split m{}, $cleartext ) {
        state $c = 0;
        # here's where I made a mistake, and wrote my decode to
        # work with my mistake. I was using $c % length $keyword
        # as the column determiner, rather than the index of the
        # letter at position $c % length $keyword.
        # the keyword 'aaaa' should give a cyphertext that's the
        # same as the cleartext.

        # If your algorithm cannot return an encrypted letter
        # that's the same as the clear letter, you have an
        # attack vector, but if your keyword is all "a" with this,
        # you have not encrypted anything.

        # and, really, long-term viability is not helped by
        # short variable names
        my $k = $keyword[ $c % length $keyword ];
        my $d = $alpha{$k};
        my $e = $alpha{$clear};
        my $f = $base[$d][$e];
        push @cypher, $f;
        $c++;
    }
    return join '', @cypher;
}

sub decode_vigenere ( $keyword, $cyphertext ) {
    my @keyword = split m{}, $keyword;
    my @base    = make_core_cypher();
    my @alpha   = 'A' .. 'Z';
    my %alpha   = map { $alpha[$_] => $_ } 0 .. 25;
    my @clear;
    for my $cypher ( split m{}, $cyphertext ) {
        state $c = 0;
        my $k = $keyword[ $c % length $keyword ];
        my $d = $alpha{$k};
        my $e;
        for my $i ( 0 .. 25 ) {
            $e = $i if $base[$d][$i] eq $cypher;
        }
        my $f = $alpha[$e];
        push @clear, $f;
        $c++;
    }
    return join '', @clear;
}

sub make_core_cypher () {
    my @alpha = 'A' .. 'Z';
    my @output;
    for my $i ( 0 .. 25 ) {
        for my $j ( 0 .. 25 ) {
            my $k = ( $i + $j ) % 26;
            my $l = $alpha[$k];
            $output[$i][$j] = $l;
        }
    }
    return @output;
}

    CLEAR:
        WRITEASCRIPTTOIMPLEMENTVIGENERECIPHERTHESCRIPTSHOULDBEABLEENCODEANDDECODE
    CYPHER:
        WKBTGKSVUILGTHBMRVEFHNPIIZXNGBEVLPDRRMAEUMRBSTOUONEDDOAUOEAACHWECXDWHCKQE
    DECRYPT:
        WRITEASCRIPTTOIMPLEMENTVIGENERECIPHERTHESCRIPTSHOULDBEABLEENCODEANDDECODE

If you have any questions or comments, I would be glad to hear it. Ask me on Twitter or make an issue on my blog repo.