Secret Meeting of Letters and Numbers: Cryptology

Cryptology is the study of “secret writing”. It deals with ciphering information: takes the letters, matches them with numbers, then these numbers are changed to letters again by a secret way. Designing this secret meeting, modular arithmetic helps a lot.

Due to increasing security problems, our need for this secret meetings has grown. Cryptology is used in many areas such as the security of banks, computer and network passwords, between messaging of persons and government foundations, etc.

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One of the earliest and simplest ciphers is the ‘substitution cipher’ which was used by Julius Caesar during his military campaigns in 100-50 B.C in Egypt. Caesar, Roman military and political leader, replaced the letters by letters three positions further down the alphabet. For example, with a shift of 3, A would be replaced by D, B would become E, and so on. We may write C (x) = x + 3 (mod 26). So, according to this ciphering method we can read the subtitle of this section: The History of Cryptology.

It is easy to break the Caesar cipher. Because, the frequency of letters changes in every language. For example in the English language, the letters E and T are usually most frequent, but in Turkish the letters A and E. By using the frequency analysis and computers we can break even the long ciphers in few seconds.

Terminology

Cryptology is the study of cryptography meaning “secret writing” (from the Greek kryptós, “hidden”, and gráphein, “to write”). Cryptology deals with both ciphering and deciphering information. While the roots of ciphering information extend to Ancient Greek, cryptology is founded by Arabians in 800s, long after that.

Cipher in English, chiffer in French, şifre in Turkish are all coming from sıfır (sat-fe-rı: bending, changing into, turning to) in Arabic language.

The meeting of letters and numbers which is known as Ebced in Arabians was used in many areas besides ciphering information. In Ebced numeric values were given to every letter in the Arabic alphabet. And the name of this method comes from the letters elif, be, cim and dal which were matched with 1, 2, 3 and 4.

First Ciphering Devices

First ciphering devices in the history of cryptology started to be used in 16^th century. But the most important one was Enigma which had determined the destiny of the Second World War. Enigma, made in Germany, was used in the military submarines and caused the Entente Powers to lose their power. However, in the last period of the war, German military used Enigma very inattentively and used uncreative ciphering letters like AAA or ABC. That is why Britain army broke the ciphered messages easily and gained power.

In fact, we can say that the ciphering systems which were used in Second World War in order to send strategic messages, the algorithms used to break the codes, the invention of ciphering and deciphering devices has resulted in the rise of computer science.

Who is using cryptology today?
Today, not only the intelligence departments and the military need cryptology for ciphering messages but also we use cryptology in our daily lives. We use it when we withdraw cash from ATMs or shop from the internet, in our computers or when we use online banking, etc.
Day by day, the mathematicians develop new encryption methods. Nowadays, AES (advanced encryption standard) is being used by U.S. government. AES has a fixed block size of 128 bits and a key size of 128, 192, or 256 bits; which is sufficient to protect classified information up to the SECRET level. For the TOP SECRET level 192 or 256 key lengths are used. And of course attacks are unavoidable where there are secret meetings of letters and numbers. But, in the conclusion all these attacks –whether successful or not- serves as an incentive to improve the encryption methods and cryptology.

A Mathematical World

Below is a ciphered text which was encrypted with a method which I derived from the substitution cipher and developed a bit. Our key to break the code is ‘A Mathematical World’. That is, the first word of the text is encrypted with A (first letter of our key), the second word with M (second letter of the key), third word with A (third letter of the key), … Here is the ciphered text:

J JVFU ZPV U TQNM KZQQ BS BSJUINFUJD: BYUFNB JMMNM, SDLQ TVCUSBDUFE, XAHQ JRIQFMIFBA PCS XJAWFVKZAH ZQHQD HMZMHIH.

Hint: For example, first word of our text is encrypted with the letter ‘A’ and the numeric value of A is 1.

A	B	C	D	E	F	G	H	I	J	K	.	.	.
1	2	3	4	5	6	7	8	9	10	11	.	.	.

You should think: “To which letter’s numeric value 1 was added to get a ‘J’ (numeric value: 10)? i.e. x + 1 = 10 (mod 26) then x = 9 which matches with I.

So, the first letter of our text is 'I'. To see the decrypted text click here.