Public Key Cryptography Protects Your Information

Posted: October 26, 2014 by uszik11 in First Steps, Security or Privacy Initiatives
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The methods of securing data are robust. Your financial transactions, health records and other sensitive information are safeguarded by strong mathematical processes. You can use these same tools yourself to keep your emails private. It is not much harder than learning a new phone and installing an app.

Usually, when your personal data is exposed by organized gangs of Russian “businessmen” or the Chinese People’s Liberation Army, it because of failures in computer security allowed by weaknesses in the programs. The cell phone companies deliver records to the NSA. The NSA does not break your ciphers. As far as we know, no one has ever cracked one of the public key methods developed since 1975. Some theoretical weaknesses have been suggested. Brute force attacks by the NSA have been hinted at, but never demonstrated. The mathematics is as immutable as the Law of Identity: A is A.  It is absolutely true that 1 + 1 = 2, always and forever.

A Crazy Idea

In the early to mid-1970s, independent researchers Whitfield Diffie and Martin Hellman at Stanford, Ralph Merkle at Berkeley, and Ronald Rivest at MIT, along with his doctoral candidates Adi Shamir and Lenard Adelman, all sought and found ways to encrypt information that were not based on any of the historically known methods. As a result, when Ralph Merkle submitted his papers to the Communications of the Association for Computing Machinery, they were rejected for denying the established wisdom of 2000 years. Working on his doctorate at Berkeley, he was told by his professors that he obviously did not know the basics of cryptography.

Codes and Ciphers

A code is a secret translation of one set of symbols for another. If we let
Handkerchief = Train
Scarf = Bus
Blouse = Plane
Red = 2:00PM
Blue = 3:00PM
Green = 3:45 PM
Then, “Thank you for the red scarf “ or “Thank you for the green blouse” could be sent via email or on a post card and the real meaning would be hidden. The weakness is in exchanging the key. Someone has to pass the translation table. However, given the security of the key table, the code is unbreakable.

A cipher is an orderly substitution. Taking the alphabet backwards, A=Z, B=Y, C=X,… turns BARACK OBAMA into YZIZCP LYZNZ. Another kind of cipher just takes the letters in turn say, every third in rotation so that HILLARY CLINTON becomes LRLTHLYIOIACNN.

Ciphers often can be broken with applied arithmetic. In English, e is the most common letter, followed by t a o i n s h r d l u… Among the complicated ciphers was the Vigenere in which a table of letter keys allowed shifting substitutions. During World War II, the Germans employed their “Engima” machine with its shifting and changeable wheels. It fell to the first of the computers, the “Bombe” of Bletchley Park and “Ultra” Project. In The Jefferson Key by Steve Berry (Ballantine Books, 2011), a supposedly unbreakable cipher finally falls to a modern-day sleuth. As constructed, it involved writing the letters vertically, then inserting random letters, then writing the letters horizontally. However, again, common arithmetic allows you to use the fact that any English word with a Q must have that letter followed by a U; and no English words have DK as a digraph. (Until DKNY, of course.) So, the cipher was broken.

Speaking to LASCON in Austin, October 23, 2014, Martin Hellman said that he and his co-workers were considered “insane” for suggesting that an encryption method could be devised in which the formulas were public. In fact, this idea had old roots.

The 19th century founder of mathematical economics, William Stanley Jevons, suggested that certain mathematical functions that were “asymmetric” could be the basis for a new kind of cryptography. Just because A=Z does not mean that Z=A. His idea did not bear fruit. However, Martin Hellman asked his colleagues in the mathematics department if they knew of any such asymmetric functions. Indeed, many exist.  They can be called “trapdoor functions” because they are easy to do in one direction, but computationally difficult in the other.  In other words, they are are unlike the four common arithmetic operations.

The Diffie-Hellman system employs modulo arithmetic.  RSA (Rivest-Shamir-Adleman) uses the totient function discovered by Leonhard Euler in 1763. In 1974, Ralph Merkle, then at Berkeley, thought of using a set of puzzles, where each one is moderately hard, but the full set of 15 becomes computationally difficult. Working together, Merkel and Hellman created a “knapsack” function in which the challenge is to put the “most important objects” (numbers) with the smallest weights (numbers) into a bag (solution set).

You can get the papers online. If you loved high school algebra, and get a kick out of crossword puzzles (especially acrostics) this will be fun. If not, just accept the fact that they work.

The salient facts remain: the cipher system is clearly described, yet stands cryptographically secure.   That is a mandate called “Kerckhoffs Law” named for Auguste Kerckhoffs, a 19th century Dutch linguist. A cryptographic system should remain secure, even if everything about it is known, except the key. Thus, in our time, you can find the mathematical theorems and computer code for public key systems. You can download almost instantly clickable applications to secure your email.

Pretty Good Privacy
A hundred years ago, codes and ciphers and the study of cryptography all were controlled by the secret services of governments. In our time, academic theoreticians publish papers. To be patented, a device must be published. And so, Phil Zimmermann took the mathematical theorems and processes of the RSA encryption algorithm and recoded them from scratch to create a new system, just as powerful, but available to anyone without need for a license. Zimmermann was threatened with lawsuits and such, but he prevailed. Today, PGP is a free product offered by software sales giant Symantec on their website here. It is something a “loss leader” for Symantec. You can get PGP from other places as well, see here.

With it, you can encrypt your emails. Know, however, that (1) you would need to be “approved” by another PGP user (easy enough) and that (2) anyone you send emails to with this also needs it to read your emails to them. Be that as it may, it is no harder than setting up a really cool Facebook page, just a bit of work and some close focus.

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