Sierpinski's shoes

Posted by Jonas Elfström Wed, 14 Nov 2007 22:50:00 GMT

There were no cross-platform windowing toolkits for Ruby so _why made one and he calls it Shoes. Not even close to 1.0, it's already yummy in a chunky kind of way and since it came from _why I simply had to try it out. Something simple.

Shoes.app :width => 1024, :height => 768 do  
  corners = [ {:x => 256, :y => 10}, {:x => 12, :y => 378}, {:x => 506, :y => 378} ]
  xpos,ypos,c = 256,10,0
  srand
  2111.times do
      c=rand(3)
      xpos += (corners[c][:x]-xpos)>>1
      ypos += (corners[c][:y]-ypos)>>1
      star xpos, ypos, 5, 10
  end
end

The result.

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The Zodiac Killer Cipher

Posted by Jonas Elfström Fri, 25 May 2007 16:31:00 GMT

The Zodiac Killer was a serial killer in the late sixties and maybe early seventies. He sent a number of letters to the press, including four ciphers or cryptograms and only one of them has been solved. The killer's identity remains unknown.

Chris McCarthy has a nice page about the cipher and he also has an ASCII version of the cipher.

Here's a small Ruby hack that calculates the character frequency using the ASCII version of the cipher. Feel free to use it if you like to have a go at cracking it!

EDIT: At this page you can have a go at cracking it real-time. I am not convinced it's really a homophonic substition cipher since the frequency analysis shows that the 340 does not have a flat frequency distribution.

It would be nice to know what cryptographic literature was available for the public in northern California in the late sixties.

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Find primes in regexp

Posted by Jonas Elfström Fri, 30 Mar 2007 05:33:00 GMT

In an earlier post the example code did find prime numbers. Recently I stumbled over a really cool regexp hack that also deals with primes. This is how you execute that regexp in Ruby:

puts 'Prime' unless ('1' * 43) =~ /^1$|^(11+?)\1+$/

Change 43 to whatever you like and you will get Prime as output if it's a prime number. EDIT: As you can see in the comments Neil Kandalonkar explained how the regexp by Abigail works.

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What one-way hash function to use?

Posted by Jonas Elfström Tue, 27 Feb 2007 16:01:00 GMT

One-way hash functions takes a message of any length as input and outputs a very large but fixed length number, called message digest or fingerprint. They can be used for "storing" passwords or as a signature that makes it possible to verify that you got the correct message.

MD5 got into problems over 10 years ago and SHA-1 could to be heading the same way. Until the new standard is published I would follow the crowd and recommend SHA-256.

Ruby
require 'digest/sha2'
quickfox="The quick brown fox jumps over the lazy dog"
Digest::SHA256.hexdigest(quickfox)

=> "d7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592"

C#
using System.Security.Cryptography;

...

 ASCIIEncoding byteConverter = new ASCIIEncoding();
 string quickfox="The quick brown fox jumps over the lazy dog";
 HashAlgorithm sha256 = new SHA256Managed();
 byte[] hash = sha256.ComputeHash(byteConverter.GetBytes(quickfox));
 crypt.Text = Convert.ToBase64String(hash);

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SETL, Ruby and list comprehensions

Posted by Jonas Elfström Fri, 09 Feb 2007 00:11:00 GMT

Someone mentioned SETL and I didn't even know what it was so I googled it. Ended up at http://en.wikipedia.org/wiki/SETL#Sample_code:

Print all prime numbers from 2 to N

  print({n in {2..N} | forall m in {2..n - 1} | n mod m > 0});

The notation is similar to list comprehension.

Interesting! In Ruby you could do that something like this:

N=42
2.upto(N) {|n| puts n if (2..n-1).all? {|m| n.modulo(m)>0} }

The SETL example at wikipedia actually iterates way too much.

N=42
puts 2
3.step(N,2) {|n| puts n if (2..n/3).all? {|m| n.modulo(m)>0} }

I realize this is not purist list comprehension, well actually it isn't lc at all. Ruby does not have lc in the same sense as Python and others, but you can do almost everything you can with lc with the fantastic collection of methods in Enumerable. If that isn't enough you could always expand Ruby with a more general support for list comprehension like described here.

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