ENCRYPTION/DECRYPTION SYSTEMS

                                                                by

                                                                KAUSTUBH JOSHI (02007018)

                                                             VIKRANT KULKARNI (02007021)

                                                             GOURAV DHAVALE (02D07009)

INTRODUCTION:

Communication is one of the most important aspects of human behaviour. The ability to

express our thoughts in a written form is a distinguishing feature of human

communication. The need naturally arises to conceal sensitive information from

illegitimate eyes. This is where the science of cryptography steps in.

Cryptography is the practice and study of encryption and decryption – encoding

data so that it can be understood only by specific individuals. A system for

encrypting and/or decrypting is a cryptosystem. These usually involve an

algorithm for combining the original data (plain text) with one or more keys –

numbers or strings of characters known by the sender and/or recipient. The

resulting output is called the cipher text. We now proceed to examine this class of

objects from a signals and systems point of view. A cryptographic system is

defined by an algorithm concerning the cryptographic system.

This system takes string characters (say decimal numbers) as input signal. These

characters are taken from a set of finite cardinality. The output signal is the

corresponding encrypted string (or decrypted string in case of decryption

systems) that need not have same number of characters as the input and whose

domain of characters need not be the same. The independent variable for both

input & output signals is position of the character in the corresponding string.

The characters represent weights attached to the position.

A cryptosystem must be invertible that is, an inverse system must exist for it

being practically useful. For, what use is an encoding system when the cipher text

can not be decoded to get back the original message? An important issue that

comes up is that a third party must not be able to decode an encoded message.

This brings in the notion of security of the system that is the degree of its

vulnerability to unauthorized attacks.

While examining an algorithm for security we must take into

account the fact that a potential hacker has complete knowledge of the

encryption system being used and only does not know the key being used. This is

the statement of the Kerckhoff’s Principle and usually is an extreme assumption.

When dealing with cryptographic systems it is important to note that the system

is represented by an algorithm which typically requires a string (‘key’) as a priori

input.

Thus, each algorithm is actually a collection of ‘m’ systems (here systems is in the

context of this course) where ‘m’ is the size of the key space of the algorithm.