Consider the following RSA key set to determine the value of d that is used as the secret key.

The provided value of p, q n and e are as follows:

Calculate the value of using the formula .

Compute the value of d using Extended-Euclid’s algorithm such that

where k is the least positive integer.

For

Therefore the value of the secret key is .

Calculate the cipher text of the message .

The formula to calculate the cipher text is .

where c is the cipher text.

Therefore, the encryption message of the message is 254 .

If Alice’s public exponent is chosen as 3, then it is insecure.

Suppose that when a same message that Alice want to send to several different people.

• Now, if Alice does the obvious thing as encrypting the message which have to send using each of their public keys and send it.

• Then eavesdropper Eve will collect every encrypted message.

Now, Eve will check if the number of messages is equal to or greater than the encrypted exponent, then in this condition Eve may recover the message.

Consider the following example:

Suppose Alice’s want to send the same message in the encrypted form to a number of different several people, where every using the same exponent and different modulo.

Suppose the eavesdropper Eve intercepts and where, .

Then,

However,

Then user consists the following:

Thus, holds over the integer and then Eves can easily obtain the cube root of to compute.

Hence, if the exponent is chosen to 3 or; then only three different encryptions are sufficient to recover the original message.

Therefore, from the above explanation it is clear that, “if the exponent is chosen to 3, then the adversary can factor Alice’s modulus n in time polynomial in the number of bits in n”