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CRYPTOGRAPHY: a fascinating topic

di Joy Osasuyi 5A OSA

The class 5^AOSA on 8th February 2019 went to a History Walk in Pavia, that took place at the Museum of Electrical Science (Museo della Scienza Elettrica).

The theme of the lesson, which was held by a Maths Austrian teacher talking in English, was cryptography.

The teacher defined cryptography as the technique that allows to "encrypt" a message making it incomprehensible to everyone except its receiver. In general the main process that is applied in cryptography is encryption that converts ordinary information (called plaintext) into unintelligible form (called ciphertext), heavily based on mathematical theory; making such algorithms hard to break by any adversary.

Decryption is the reverse, moving from the unintelligible ciphertext back to plaintext. A fundamental role is given to the key that is a secret, usually a short string of characters, which is needed to decrypt the ciphertext.

The teacher often used the names Alice ("A") for the sender, Bob ("B") for the intended recipient, and Eve ("eavesdropper") for the adversary.

There are two kinds of cryptosystems: symmetric and asymmetric.

In symmetric systems the same key (the secret key) is used to encrypt and decrypt a message. Data manipulation in symmetric systems is faster than asymmetric systems as they generally use shorter key lengths. Asymmetric systems use a public key to encrypt a message and a private key to decrypt it.

There are many cryptographic techniques and among these the two mentioned by the teacher are: the technique based on the replacement of each letter of the starting text, in the ciphertext, with the letter which is found, in the alphabet, a certain number of positions after and also the Visual Cryptography that is used for secure communications, the sender will distribute one or more random layers 1 in advance to the receiver. If the sender has a message, he creates a layer 2 for a particular distributed layer 1 and sends it to the receiver. The receiver aligns the two layers and the secret information is revealed, this without the need for an encryption device. For example if the original image is white, in its encoded version, the sub-pixel pair used in a share is the same as that used in the other share, so that the overlay generates a pair in which one sub-pixel is white and the other is black. The color black is represented with the value "1" while white with "0.

Cryptography uses a lot of Modular Arithmetic, is a system of arithmetic for integers, where numbers "wrap around" each time they reach multiples of a certain value n, called modulus.

If the product (a x b) / sum (a + b) is not a multiple of n, we must calculate the difference between the result and the multiple closest to the result.

Example:

7 + 6 = 13 ≡ 3 mod (10)

5 · 4 = 20 ≡ 2 mod (6)

We were the first students to listen to the lesson of this Austrian teacher and we found it really interesting even if not always easy to follow as it dealt with mathematical concepts in English.

The following day on 9th February 2019 at school there was a conference held by our ICT teacher, Letizia Valensisi, who talked about Artificial Intelligence and the figure of Alan Turing.

Alan Turing is considered the father of theoretical computer science and artificial intelligence.

Turing was very influential in the development of theoretical computer science, providing a formalization of the concepts of algorithm and computation with the Turing machine, which can be considered a computer model for general use

During the Second World War, Turing worked for the Government Code and the Cypher School (GC & CS) at Bletchley Park, the UK coding center that produced Ultra intelligence. For a while he led the hut 8, the section that was responsible for the German naval cryptanalysis. Here he devised a series of techniques to accelerate the breakdown of German ciphers, including improvements to the method of pre-war Polish bombs, an electromechanical machine capable of finding the settings for the Enigma machine.

At the Museum in Pavia we also had the opportunity to see one of these machines.

The world of cryptography is a fascinating one and the school gave us two important opportunities to know something more about it!

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