The History and Mathematics of Codes and Code Breaking

Author: schlunsg

Dead Pixels

Too Far, and yet Not Far Enough

One passage that I particularly liked for its relevance to modern day encryption, is when Randy and Avi are communicating using Ordo, a program that helps them encrypt their messages. It uses modern encryption where the user selects a key length and creates a key, which is used to encrypt the messages. The longer the key, the more other possible keys there are and the harder it is for someone to crack. In the book, Ordo gives the options of 768, 1024, 1536, 2048, and 3072 bit keys. A 768 bit key by itself is very difficult to break and would take a lot of time. However, Randy and Avi decide to use a 4096 bit key, which is effectively unbreakable. For reference, each additional bit added (like 768 to 769 bits) doubles the total number of possible keys, so 4096 bit keys are not just a lot harder to break, they are literally unbreakable in comparison.

Dead Pixels

Dead Pixels by coda

This is very similar to the RSA encryption we have discussed in class, as far as the prime numbers involved and the time it takes to crack. So the question is, how far does one really need to go to create a key? As Randy says, “it would take longer than the lifespan of the universe” to break the key (Page 54). Even with the advancement of technology at the rate it moves, a key only needs to last so long and surely 4096 bits accomplishes this completely.

This passage added to my understanding of the encryption by helping me get a perspective on just how big these keys are and how safe they are as far as ability to be broken. Like I said, these topics that deal with modern day encryption by far interest me the most since they are basically what we continue to use today. I feel that the more we know about the encryptions that we actually use, the more safe we can keep our information.

Image Credit: Dead Pixels by coda

Right to Security?

Cryptography has always been about outdoing and outperforming the cryptanalytic efforts of others, trying to create an unbreakable, perfectly secure code. Today with the help of computers we have been able to get closer than ever before, creating encryptions that cannot be broken by any normal means. However, now is also the first time that the efforts to create such an unbreakable cipher are being held back. The National Security Agency, in order to stay on top cryptographically, limited the Data Encryption Standard to something they could crack if necessary. According to Singh, one of the first examples of this was back in the 1970s, when Horst Feistel created Lucifer, the strongest encrypting machine of its day. However, before it was adopted, the NSA argued to limit the number of keys such that no personal computer could break it, but the NSA could if it needed to.


This seems relatively reasonable. When necessary, the government can intervene and get the information they need, but it would be sufficiently hard that they would not be taking information all of the time. But wait, what about the right to privacy? Shouldn’t we have a right to an unbreakable encryption, if we so choose? This comes down to the increasingly important argument of privacy over security. Are you willing to sacrifice some of your privacy (the NSA can see everything you do if it wants) in order to grant a little bit of security?

I think not. If the NSA can crack the encryption, I would bet that there are others who can as well, be it other governments or something more sinister. Obviously the vast majority of the population has nothing even vaguely interesting to hide in the eyes of the NSA, but the fact that they can look into the personal life of any person they choose is frightening.

Photo Credit: BramstonePhotography

Scale of Justcie

Where Do We Draw the Line

Throughout Little Brother by Cory Doctorow, I found myself torn as to who I should support. Several times I found myself questioning what I believed and what I would do. In chapter 13, however, I had no trouble siding with Marcus during his discussion in class about suspension of constitutional rights.

Scale of Justcie

When Mrs. Anderson brought up the hypothetical situation where a police officer went beyond what his search warrant allowed for, and found indisputable evidence to prove the person is guilty. This is a classic question of whether the law or justice is more important. She asks, “Should the bad guy go free?” Should he? No, but he must.

In the same way that the Miranda Rights prevent police from using evidence gained without the other party knowing his or her rights, a police officer cannot use evidence gained in an illegal search. No one would ever tell you that he deserves to go free, but because of how our system works, that is the way it must be. The day we start bending the rules is the day we can no longer trust the rules to be on our side.

The fact is that without rules we are a bunch of uncontrollable creatures who act selfishly whenever possible. Either we have rules or we do not, there is no in between. If rules are not absolute, then there is no way to enforce them with a straight face. Obviously there are times when certain rules must be suspended (state of emergency), but there are rules in place that explain how that works. The problem arises when a government suspends rules/rights that they have no right to suspend.

The Constitution is a living document, and I agree that changes have to be made to it in order for it to continue to function as intended. However, the the way the teacher describes it is not that. She seems to believe that you take the Constitution as guidelines rather than rules, which is just downright false. If you do not like what the Constitution says, you have to change it. You cannot just ignore it.

Picture Credits: Scale of Justice 2 New: Original by DTR, Derivative by Agradman

The Mystery of the Unknown

Beale Papers Pamphlet
The Beale Cipher is indeed one of the modern mysteries of cryptography, and the fact that it is mostly unbroken can either mean one of two things: the answer continues to allude the thousands of cryptanalysts and treasure hunters who have tried thus far, or the cipher is indeed faked, and there is no actual solution. If it is indeed the latter and the cipher is a fake, then there is no reason for people to continue. There would be no treasure for the treasure hunters, and there would be no actual solution to find for the people who just want to solve the cipher.

However, the fact is that no one knows for sure whether the cipher is a fake or not, meaning that there is a chance that there is an actual solution, and maybe even an actual treasure.

It is unlikely, however, that at this point in time the actual worth of the treasure has any significant effect on the desire to crack the code, but it is possible. The fact that so many people have failed to crack it means that no one person can really expect to solve it, hence the likelihood they solve the code and find the treasure must be really small. Therefore, the majority of the motivation for looking for the solution is probably just the mystery that surrounds the code, the fact that it is unsolved. These are the types of people who are doing it for fun, because they can. What better reason is there than that.

Image Credit: “Beale Papers” Wikimedia Commons (Public Domain)

Syllable Substitution

The Great Cipher of Louis XIV was truly a remarkable cipher, and its longevity only attests to its success. Antoine and Bonaventure Rossignol were the masterminds behind its brilliance, and with their death brought the end of its effective use. During the time of its use, the Rossignols lived adjacent to Louis XIV, since they were the only ones who could effectively use it. The fact that it took two centuries to crack is beyond remarkable, and it deserves praise.

The key to its success and difficulty was that the plain text was not explicitly the 26 letters of the alphabet. Most monoalphabetic and polyalphabetic substitutions start with the initial 26 letters (a, b, c, … z) as the original plain text and substitute each letter with another letter (or in the case of polyalphabetic ciphers) or maybe a couple letters. But the fact is that the plain text and the cipher text will be limited to the 26 letters of the alphabet, no matter the method of cipher used. This cipher was unique compared to others because the original plain text consisted of all of the individual sounds or syllable used, hence there were many, many more original plain text “letters” compared to an ordinary substitution ciphers. Therefore numbers had to be used rather than letters because there was no alphabet large enough to contain all of the syllables in the language.

Additionally, the Rossignols added traps within the cipher, such as numbers that adjusted adjacent numbers (like removing them entirely). Numbers also often translated to single letters rather than syllables which threw off people who attempted to decipher it. These key differences made the code inefficient since there were so many different “letters” that a person needed to keep track of, but at the same time made it virtually uncrackable to even the most scholarly people. If it were not for the sheer size of the pool of the total numbers used, people would have undoubtedly continued to use it.

Understanding: From Past to Present

It is no surprise that cryptography and cryptanalysis require at least a basic, and in most cases an elevated, understanding of mathematics, statistics, and linguistics. Back in the time before cryptography had been developed, such understanding was minimal if anything, and hence it is no surprise that cryptography was as well. As time passed, scholars in these civilizations began to unlock the secrets of cryptanalysis, but it was not until the civilization as a whole had grasped these concepts of math, statistics, and linguistics that cryptanalysis could be really put to good use.

Ever since then, all advanced civilizations have emerged with these basic understandings that we take for granted. Unlike in the time when cryptanalysis was first appearing, the average citizen in most of the modern world can read, can do simple math, and has a basic understanding of statistics. These are the minimal skills required to understand cryptography, and thus it is no surprise that even an amateur of today’s world can understand and work with the advanced cryptography that existed back in the earliest civilizations. As we have seen, college students can easily grasp basic substitution ciphers with relative ease, and these basics do not even require the understanding of math and statistics – purely an understanding of linguistics at its most basic form. Thus, the application of frequency analysis seems like an obvious and easy step for a young cryptologist in today’s world, whereas when it was first invented, it seemed like a break through that would (and did) change how man viewed cryptography forever.

At the core, an amateur today is as good as a skilled cryptologist hundreds of years ago because today’s civilization has a minimum understanding that surpasses the understanding of older civilizations by huge strides. We all have a better understanding of the skills required, which allows us to grasp the advanced methods significantly quicker and at a younger age than was ever imaginable. It is no surprise that a highly advanced method of the past is a commonly used technique today when you consider the differences in understanding between the past and the present.

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