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# Cryptosystems Based on Discrete Logarithm

Masters

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Technology

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Any data we input into the computer with the help of the key board is converted into numbers of the binary system in accordance with ASCII code. For instance the character 'A' is entered as 10100001 in the binary notation (Subramaniun, 140), which corresponds to the number 161 in the usual decimal notation.

## Introduction

Rather it will be sent as the binary string corresponding to another number which depends on the number 161 according to some fixed rule. For example we can subtract 161 from the largest 3-digit number 999 and send the result 838. Thus the rule for encryption is:

But there is a drawback of using this method of encryption. The receiver has also to be conveyed what rule has been used for the encryption, so that he can decrypt it. If some hacker in between cracks the information about this rule, then it is a trivial job for him to get the number 161 back from 838. For, he will easily deduce from this rule for encryption, the rule for decryption:

Therefore we make use of an ingenious technique. This technique makes the decryption of the encrypted message very difficult (if not impossible) for any third person (hacker). In order to know the technique, we need to learn some of the mathematical concepts. So first of all we take up these.

Given two natural numbers and an integer n, then by the modular exponentiation of b to the base a, which is symbolized as, we mean obtaining the remainder on dividing. Thus, for example,, on being evaluated yields 7. Observe that we can also write using the above concept of congruence modulo m.

Further given two natural numbers and an integer n, then the smallest (non-negative) integer x (if exists) such that, is known as the discrete logarithm of b to the base a. ...

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