Cryptography Series: Lecture 0

Manoj Twarakavi
Game of Life
Published in
5 min readOct 3, 2020

Preface: This is a series of lectures on Cryptography starting from the basics. The intended audience are novice learners with at least a high school math background.

Cryptography is the study of communication in the presence of an unknown third party entity (known as an ‘adversary’ or ‘interceptor’). The field of cryptography is an embodiment of many problems like encryption, decryption, authentication, user identification etc. to name a few. All these concepts are the foundation in developing confident protocols for communication through an insecure channel. It is thus the cornerstone in Communications & Security.

Classical Encryption Techniques

Let us understand encryption through a basic example.

The earliest known use of cryptography is the substitution cipher and the simplest was by Julius Caesar. The Caesar cipher involves replacing each letter of the alphabet with the letter standing 3 places further down the alphabet.

e.g., plain text : pay more money

Cipher text: SDB PRUH PRQHB

Note that the alphabet is wrapped around, so that letter following “z” is “a”.

For each plaintext letter p, substitute the cipher text letter c such that,

C = E(p) = (p+3) mod 26

A shift may be any amount, so that general Caesar algorithm is,

C = E (p) = (p+k) mod 26

Where k takes on a value in the range 1 to 25. The decryption algorithm is simply, P = D(C) = (C-k) mod 26.

A more complex scheme is to write the message in a rectangle, row by row, and read the message off, column by column, but permute the order of the columns. This is known as Row Transposition Cipher. The order of columns then becomes the key of the algorithm.

e.g., plaintext = meet at the school house

Key = 4 3 1 2 5 6 7PT = m e e t a t t h e s c h o o l h o u s e

CT = ESOTCUEEHMHLAHSTOETO

In 1948, Shannon developed this theory on perfect secrecy based on Information Theory. In this theory, the adversary is assumed to have unlimited computational resources. Shannon showed that secure(properly defined) encryption system can exist only if the size of the secret information S that A and B agree on prior to remote transmission is as large as the number of secret bits to be ever exchanged remotely using the encryption system.

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Modern Cryptosystems

A cryptosystem is an implementation of cryptographic techniques and their accompanying infrastructure to provide information security services. A cryptosystem is also referred to as a cipher system.

A Simple Cryptosystem Model

The illustration shows a sender who wants to transfer some sensitive data to a receiver in such away that any party intercepting or eavesdropping on the communication channel cannot extract the data. The objective of this simple cryptosystem is that at the end of the process, only the sender and the receiver will know the plaintext.

Components of a Cryptosystem

The various components of a basic cryptosystem are as follows −

Plaintext — It is the data to be protected during transmission.

Encryption Algorithm — It is a mathematical process that produces a ciphertext for any given plaintext and encryption key. It is a cryptographic algorithm that takes plaintext and an encryption key as input and produces a ciphertext.

Ciphertext — It is the scrambled version of the plaintext produced by the encryption algorithm using a specific the encryption key. The ciphertext is not guarded. It flows on public channel. It can be intercepted or compromised by anyone who has access to the communication channel.

Decryption Algorithm — It is a mathematical process, that produces a unique plaintext for any given ciphertext and decryption key. It is a cryptographic algorithm that takes a ciphertext and a decryption key as input, and outputs a plaintext. The decryption algorithm essentially reverses the encryption algorithm and is thus closely related to it.

Encryption Key — It is a value that is known to the sender. The sender inputs the encryption key into the encryption algorithm along with the plaintext in order to compute the ciphertext.

Decryption Key — It is a value that is known to the receiver. The decryption key is related to the encryption key, but is not always identical to it. The receiver inputs the decryption key into the decryption algorithm along with the ciphertext in order to compute the plaintext.

For a given cryptosystem, a collection of all possible decryption keys is called a key space.

An interceptor an attacker is an unauthorized entity who attempts to determine the plaintext. He can see the ciphertext and may know the decryption algorithm. He, however, must never know the decryption key.

In this introduction lecture, I have given an overview of the basic terminology of Cryptography. In the next lecture, we shall discuss on Symmetric & Asymmetric Cryptographic Systems.

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