A bit about Code-Breaking… Encryption Theory 101

Recently, the skeleton of a carrier pigeon was found in a chimney in Surrey, England, with a message canister still attached.  The canister contained an encoded message of 27 groups of five letters, that has “stumped” code-breaking experts.  Here’s a link to the article.

It’ll never be cracked.

It’s not that today’s code-breakers aren’t up to speed, or that the codes of WWII were that sophisticated.  It’s that the key space exceeds the message space.

This type of code is almost certainly a substitution cypher.  In other words, each group of five letters is probably a simple substitution cypher, in that each letter is a substitution for a different letter.  Substitution cyphers could be changed on a regular basis, even daily, by agents in the field, using information contained in dates and a simple algorithm.  As they can be cracked using statistics, particularly when the message is long enough, it’s only intention would be to have hidden what lay beneath.  The good news is that if what’s underneath is gobbledygook, it can’t be cracked by statistical means.

But that’s not why this will never be cracked.  If the only thing at play here were a simple substitution cypher, any laptop could crack it in minutes, if not seconds.  However, if the underlying message is itself scrambled in a different manner, the NSA’s best supercomputer could work on it for decades and find nothing but gobbledygook.

In addition to the substitution, the encryption almost certainly includes transposition algorithms, again, capable of being memorized by agents in the field.  These would be more complex, however, and would probably not have been tied to dates.  These transposition algorithms may very well have been agent-specific, meaning that if any individual agent was compromised, messages encoded by other agents would have remained safe.  This is not unlike modern RPK systems, whereby each individual has a public key they share with others to encrypt messages, only the intended recipient’s private key can decrypt them.  RPK systems are most widely used in securing e-mail.

But that’s not why this will never be cracked!  A third layer of encryption again goes back to substitution, but it’s not a substitution cypher.  Instead, it involves the use of code words, such as using “apple” instead of “Arnheim,” or “to” instead of “from.”  Thus, “Sally sells seashells by the seashore” might initially be encoded as “horses run planters under the stars.”  Contrary to popular misconception, no supercomputer in the world can decode this simple use of codewords, not without a boatload of additional information, including a bunch of other similarly-encoded messages and loads of historical operational data.  As with the substitution cypher portion, each agent probably had his or her own “dictionary,” that set of tables or code book with which they encoded the message and substitution cyphers.

Naturally, all of this becomes incredibly complicated back home, except for one thing:  They had ways of knowing which agent sent the message.  That may have been something as simple as an apparently random set of letters in, say, the 13th block, which may have been “siuev” three weeks ago, but has rotated every week, perhaps by one letter in the first digit, three letters in the second, two in the third, five in fourth, and four in the fifth, so that this week the 13th block reads “uoicd.”  Next month, all agents might be using the 11th block.  Who knows?  The folks at Bletchley Park knew.

The reason this worked so well is quite simple:  If each agent in the field has their own code book, transposition algorithm, and substitution cypher, it would have taken the best cryptologists months, if not years, to decode the message, and only then if they also had both the operational data and were able to make the suspected agent talk.  Yet an agent capable of decent memorization could learn these techniques, including their personal substitution cypher and code book in a week or two of intensive study.

So, the next time you see some secret agent at the movies crack a code in minutes with a computer, remember this:  “If the algorithm is unknown, it can’t be cracked,” as well as it’s corollary:  “Even if the algorithm is known, provided the key space is larger than the message, it can’t be cracked.”  And by “can’t” I don’t mean “in a reasonable period of time.”  I mean “ever.”

Some of you may be wondering, “How can I encode my messages today?”  Well, you can either invent your own encoding algorithm, which might be fun, but unless you’re an expert, will probably not be very secure.  Alternatively, some third-party e-mail systems such as Mozilla’s Firefox (my favorite) have third-party plugins such as Enigmail which do a fair job of securing your messages from prying eyes.  Enigmail uses triple-DES, which is decent, but child’s play for the NSA computers due to some inherent flaws in the DES standard.  Thunderbird also includes the ability to use certificates for both authentication and encryption, which is good enough for securing corporate communications, and the latest versions include the ability to use AES (Advanced Encryption Standard).  If implemented properly, the security is on par with that used by the DoD for material up to and including Top Secret.

Heart Attack! Save a Life – Know how to use an Automated External Defibrilator (AED)

Without going into the statistics, millions of people, both men and women, suffer from a heart attack every year.  You do NOT need to be “CPR-certified” to help save their lives!  That’s a misnomer, one which might very well cost them their lives if you’re too afraid to act.

Automated External Defibrilator
Automated External Defibrilator

Whether you choose to do CPR, use an Automated External Defibrillator (AED), or merely call 911, the most important thing you can do is to DO SOMETHING.  If you choose to do nothing, regardless of the reason whether it’s fear of hurting them or fear of legal liability, remember this:  You still have made a choice.  It’s the poorest choice you could make, but it was your choice to make, and you made it, so you’ll still have to live with the consequences.

Here’s a better choice:  Watch this short video!  It takes you through the basics of approaching a heat attack victim, calling 911 if you discover they’re not responding or breathing correctly, and shows you how easy it is to use an AED.

Remember:  Do SOMETHING!  Help save a life!

Quick LaTeX

I’ve added a new plugin which allows me to display math symbols and graphs.  Walla!

At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:
f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
where $h$ is some step.
Then we interpolate points $\{(x_k,f_k)\}$ by polynomial
\begin{equation} \label{eq:poly}
Its coefficients $\{a_j\}$ are found as a solution of system of linear equations:
\begin{equation} \label{eq:sys}
\left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
Here are references to existing equations: (\ref{eq:poly}), (\ref{eq:sys}).
Here is reference to non-existing equation (\ref{eq:unknown}).

\quicklatex{color=”#00ff00″ size=25}

\addplot3[surf,domain=0:360,samples=40] {cos(1.77245385*x)*sin(1.46459188*y)};

If I won the lottery…



If I ever win the lottery, the first thing I’m going to do is hire a lawyer to handle 100% of the transactions, thereby keeping the fact that I won completely anonymous from the public eye. I might even hire three lawyers, in layers, in case one or two layers are penetrated.

Next will be a a CPA to minimize the taxes, a CFA or CFP to help me put it where it’ll bear the greatest after-tax returns throughout my expected lifespan.

Finally, I’ll hire both a sports nutritionist and a personal trainer to help me maximize both the length and quality of my lifespan, and that’s all BEFORE we receive the check.

That’s what I’d do with the initial proceeds from my lottery winnings.  Then, the work begins:

  • Physical: At the gym every day
  • Mental: Going back to school to finish my masters and considering finishing my undergrad in engineering (I have a B.S. in Finance) followed by graduate-level work in engineering or related technical field.
That will keep me busy for the next five years, at which point I’ll use the lottery funds to open a new company to deliver fast, high-quality, yet inexpensive personal aircraft to the world.Serious, Cessna! You deliver the first new prop-driven general aviation aircraft in three decades and it STARTS at $325,000? Several of your competitors are fielding aircraft with similar seating, payload, velocity, and range for HALF that amount. That and and I think general aviation absolutely MUST switch to engines which burn jet fuel, which is both more widely available around the world, and far cheaper than avgas.
Rolls-Royce just came out with a turboprop geared towards the generational aviation market. At 225 lbs, it develops 320 shaft horsepower, perfect for turning most four-seat, high-velocity pressurized aircraft (250 to 350 kts) into fuel-sipping 16 mpg cross-country speed demons.

The Unbelievable Depravity of the Democratic Party – Denying Israel’s Jerusalem

Here’s one link.

And here’s the YouTube video.

Incredible.  Unbelievable.  Are you one of those who think Obama might try to stay in office even if he looses the election?  If what just happened at the Democratic National Convention is any indication, I’d say it’s a very distinct possibility.

So what happened?  Well, three things, really.

First, the the Democrat Party did not recognize Jerusalem as the capitol of Israel.  I think they were going with Palestine, the very idea of which violates the UN’s 1947 declaration, probably the first and last thing the UN ever got right.  In their attempts to deny Israel’s birthright, the DNC was also violating several thousand years of very well recorded history.  Did they care?  Of course not.

Second, Governor Strickland’s motion to recognize Jerusalem as the capitol of Israel was a huge surprise.  Why would they even need to propose such a motion?  Well, the answer is quite simple.  It was the official position of the Democrat Party that Jerusalem was NOT the capital of Israel.  Yep.  Our friendly 9/11 terrorists have made THAT much of an inroad into American politics.  Their infiltration of the Democratic Party is huge.  It’s massive, and the President himself is their crowing achievement.  The problem is, he’s not a Christian, nor is he qualified to be our President.  He was born in Kenya, was raised as a Muslim, and has long-term ties to many terrorist groups, most notably the Muslim Brotherhood.

Third, the proposal was necessary to maintain Obama’s credibility as a candidate.  No sane Christian or Jew would ever vote for a President or party that refused to recognize Israel, right?  Of course not.  Yet that’s exactly what Obama and the DNC were trying to do.  Some relatively sane individual stepped forward and said, “If we don’t do this, officially, you’re going to lose the election.”  He was right, and the measure was put to a vote.

Amazingly, the delegates are so far gone they shouted it down.  Did you listen to the YouTube video yet?  Listen to it!  I’m not asking you for donations.  Just bend your ear for a couple of minutes.  Did you hear it?  The delegates did NOT want the measure adopted.  The Chair ruled otherwise, because he knew that if the DNC refused to recognize Israel, they were ruined, and Obama would never be reelected.

The lady advising the speaker got it right:  “You’ve got to let them do what they’re going to do.”  That is, after all, the American way.  Yet, they did not.  The DNC lied, this time to their own lawfully-elected delegates.

If they’re so swift and blatant about lying to their own party, what in the world do you think they’ll do to the rest of America?  Do you really enjoy being screwed over six ways to Sunday?

I don’t.

The Failure of the Two-Party Election System and Why We Need +/- Voting

The Failure of our Two-Party Election System

Our two-party system of politics is failing due to Polarization.  Historically, political parties in the U.S. held some common ground.  During the earliest years of our country, for example, we had the Federalist Party, founded by Alexander Hamilton with the help of urban bankers and businessmen, and the Democrat-Republican Party, organized by Thomas Jefferson and James Madison in 1791, which its members referred to simply as the Republican Party.

Both supported an American Revolution, but the difference is the Federalists desired a strong central government, with state’s rights all but completely disappearing, while the Democrat-Republican Party did not.  Some Federalists did not even want governors to continue, and without opposition, the thirteen original colonies would have become little more than thirteen counties of the State.

FYI, the term “state” is synonymous with “country,” and some of the thirteen original colonies had established themselves as independent states i.e. countries, including the negotiation of treaties with other nations as well as between one another.  Thus, the United States was, in its infancy, much like the EU is today – a collection of independent and sovereign nations, or “states,” who had agreed to give up some of their autonomy and authority for the purpose of facilitating both commerce and a common defense, while retaining most of their autonomy and authority to run their own affairs within their own borders.

Over time, these two parties and morphed, changed names, and have died and been reborn under new names.  Today, their closest relatives are the Democratic Party and the Republican Party, with the Democrats more closely aligned with the old Federalist Party and the Republicans more closely aligned with the old Democrat-Republican party.

The problem with our two-party system is that it’s been flawed from start, and the root cause and reason has to do with the way we vote.

The Flaw:  Our +Only Voting System

With getting into the nuances of the Electoral College, we have a +Only Voting System here in the United States of American.  In fact, this is standard throughout the world, though only by knuckle-dragging default, and not by intelligent design.  Basically speaking, no matter how many options are available, each voter can only cast one vote, and then, only for one option.

The problem occurs when you have three strong candidates but two of those candidates hold similar views.  Those holding similar views will split the vote and lose the election, even if they would have been able to win had there been no similar candidate.

Let’s put this into more mathematical terms, with three candidates, A and B (both conservatives) and C (a liberal).  Let’s also assume the voters as a whole prefer voting conservative, say 60%.

Since most of the voters prefer a conservative candidate to a liberal candidate, the conservative candidate should win, right?  Nope.  The conservative candidates will split the vote, each getting 30%, while the liberal candidate will receive a winning 40%.

Another problem occurs when you have two strong candidates splitting the vote (A and B) and a splinter candidate (C) who pulls more votes from one candidate than the other.  If A & B would have split the vote 50-50 before the arrival of C, but C pulls just 1% of the vote from A but 2% from B, then A will win with 49% of the votes, B looses with 48% of the votes, and C (who never stood a chance in the first place) also looses with a meager 3% of the vote.

Rationally, if both B & C’s goals were united to defeat candidate A, then C should have withdrawn from the race.  Not all candidates are rational, however, and people like Ross Perot and his supporters idiotically and quite foolishly helped hand the election to the Democrats.  The same thing may very well happen if Ron Paul decides to run as a write-in or independent.  I can’t even admire his drive because he’s losing sight of the forest through the trees.  If the mission is to defeat Obama, the only rational choice is to drop out of the race completely and allow the far more likely candidate, Mitt Romney, full access to those conservative votes.

That’s part of the problem.  The other part involves one of polarization, the likelihood that the beliefs of a two-party system will tend to diverge over time, not only as a whole, but on each and every point.  The main cause is lack of political diversity, which encourages party politics i.e. voting the party line instead of the conscious of the elected representative.  Those who don’t consistently vote the party line are viewed as weak by the party and are usually replaced with a more polarized candidate.

The end result is that a single-vote system encourages polarization, which in turn leads to the rise of two predominant and highly polarized parties who’re incapable of working together rationally to accomplish much of anything.

The Fix:  A +/- Voting System

A +/- voting system largely negates polarization, thereby removing the drive towards a two-party system.  Put simply, each voter is allowed to cast a single vote for each and every mutually-exclusive option, but that vote can be either a + vote or a – vote.  If the individual mis-votes, their vote doesn’t count, but modern voting kiosks, but in general elections as well as Congress, would enforce these rules in order to count the maximum number of votes.

Let’s see how this works in one of our previous examples, with the popular vote split evenly between two conservatives but with the liberal pulling in strongly with 40% of the vote.  In a perfectly polarized world, the conservatives would each get 30%+ votes and 40% – votes, while the liberal receive 40%+ votes and 60%- votes.  Thus, each conservative would wind up with -10%, but the liberal would wind up with -20%.  The conservatives would tie and perform a runoff election.

Now let’s see how this would work in the case of a weak third candidate pulling more votes from one candidate than the other.  Originally, it was:

 If A & B would have split the vote 50-50 before the arrival of C, but C pulls just 1% of the vote from A but 2% from B, then A will win with 49% of the votes, B looses with 48% of the votes, and C (who never stood a chance in the first place) also looses with a meager 3% of the vote.

Now, however, we have A and B both receiving 50%+ votes and 50%- votes, while C receives 3%+ votes (1% from A, 2% from B), but a whopping 49%- votes from the A folks and 48%- from the B folks.  In short, the C candidate, who never stood a chance to begin with, never stands a chance.

But that’s in a “perfectly polarized” world, and with the +/- voting system, most people will not give a + vote to their best candidate and a – vote to everyone else.  Instead, they’ll give a + vote to every candidate they feel is qualified for the position, and a – vote only to those candidates who they feel are unqualified.

This system is used with great success in the business world, and it works like this:  Let’s say a company has a limited amount of resources, and is faced with seven different mutually-exclusive investment opportunities, each of which has both tangible (financial) and intangible qualities associated with it.  Proposals are drafted for each of the opportunities and are reviewed by the board of directors.  They vote on these projects using the +/- system, and the results are rank-ordered.  The limited funds are then given to the projects by rank order.  If any project needs more funds than remain, they go down the list to see if another, smaller project is available.  At no time, however, are funds given to projects with a net negative vote, because those projects are almost always those which will either result in a net financial or intangible loss i.e. bad for the company regardless of how much cash is lying around.

Interesting enough, this approach has vast implications for how Congress is run, as well.  Projects are voted on based on their own merits, and they’re funded only insofar as their merits and the availability of funding dictates.  Even if one to a few state’s representatives attempt to game the system on any particularly issue, the members from the other 49 states will largely avoid any such gaming as they have no fight in the matter.  They will not avoid the matter, however, and will vote according to what’s best for the country as a whole.

In summary, our two-party system is broken because the way we vote is broken.  Fix the way we vote, both in general elections, as well as in Congress, and we’ll have fixed, if not eliminated, the two-party system, but we’ll also have fixed Congress, the budget, and many other ails in our country.

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