Cracking the Code

On Mar. 29, Dr. Paul Estes, PSU Professor of Mathematics, Emeritus, held a discussion sponsored by the Society for Scholarly Dialogue on the topic of cryptology.

Cryptology is the science of encrypting and deciphering secret messages and financial transactions. With its intriguing name, it is just the sort of topic that would draw the attention of a scholarly dialogue audience, and as obscure as this topic may seem it is quite relevant in modern day society.

Estes, a war veteran, specialized in cryptology in the US Army Signal Corps, and after completing an ROTC program, was sent to Germany for three years. While there, in Cold War times, Estes worked in a succession of vans carrying crypto equipment that all played a part in the encryption process; relaying and carrying messages.

Cryptology has been a facet of war since the time of Julius Caesar whose encryption method, rightfully named the Caesar Cipher, was created.

Its presence and utilization was essential to a major break in World War II and even the war's eventual outcome. During this time period, the encryption machine of choice was the German-made Enigma. 

At this point in the war, Estes states, "In the Atlantic, [German] U-boats were sinking British and American ships."

A stroke of luck fell upon the British when one of their destroyers was able to take down a U-boat. British soldiers went down the U-boat's hatch and there they found the Enigma.

It was sent back to land where, according to Estes, "cryptologists analyzed what was captured and succeeded in breaking the Nazi code." This aided in intercepting crucial messages and gave the allies an advantage.

After the attack on Pearl Harbor, the battles in the Pacific Theater were affected greatly by cryptology. As stated by Estes, "For the first time, Navajo Indians were recruited to develop a code based of the Navajo language."

The complexity and obscurity of this language made it impossible for the Japanese to break American encryption. "They were stymied," Estes adds.

The Navajos Island hopped with the marines and utilized their own spoken encryption to relay messages. This eventually played a big role in winning the war for the allies.

Even in the iconic picture at Iwo Jima, among the marines there are Navajo "code-talkers."

In regards to use in the military, Estes summarizes crypto as, "constant leap-frogging to get ahead of the adversary," which is exactly what took place during World War II.

The variation of ways to encrypt a message makes the process seem very daunting, and breaking those encryptions even more so.

Four major methods of encryption touched on by Estes besides the Caesar Cipher were, the Multiplicative Cipher, Affine Cipher, and Frequency Cipher which each require the use of various math formulas. 

"There is a lot of guess work and trial-and-error," Estes reveals. A statement which, when taking into consideration the amount of math involved, would only makes sense.

So how, besides in militaristic use, is cryptology used today? What makes this topic relevant to PSU students and faculty of the 21st century?

As previously mentioned in the definition, cryptology is used not only for encrypting and deciphering secret messages, but for financial transactions as well.

Nowadays this financial security taken place in the for of the RSA Algorithm invented by professors Ron Rivest, Adi Shamir, and Leonard Adelman at MIT in 1997.

This encryption method uses simple prime numbers and a public key equation of n=pq to crack its code. Not only is the RSA Algorithm used in the Pentagon, CIA, and NASA, but it is used for businesses as well, such as the Chase Manhattan Bank, Boeing, and Exxon, to name a few.

Estes concluded his dialogue with the statement, "A common misconception about math is that everything has already been figured out."

With its constant use in cryptology and the discovery of new formulas to enhance those encryptions, one can only agree with Estes, that indeed, everything has not already been figured out, math is always evolving.