Step 1. Find two prime numbers, and , such that , . Compute .

You have taken , , .

Step 2. Find an integer such that the map with is bijective on the set of invertible elements of . (You must take 10000 .)

You have taken .

Step 3. Using as the public key of an RSA cryptosystem, what is the private key, that is, the integer such that ?

Suppose that in a secured communication, your partner has sent you a couple as the public key of an RSA cryptosystem, where

.

Now suppose that you have a message to sent to him. This (original) message is represented by the following number.

What is the corresponding crypted message that you should send? (The last number must be between 0 and *N*-1.)

We have two prime numbers, and . Let

Take such that the couple forms the public key of an RSA cryptosystem.

Step 1. Compute the prive key, that is, the integer such that *x*
is the inverse of *x*
in
. (Among the choices of , you must take the smallest positive integer.)

Yes, .

Step 2. Using the public key
, your partner has sent you the following crypted message (number). What is the original message (number)? (This must be a number between 0 and *N*-1.)

.

You notice that the key is too short, so that you can decrypt the messages without knowledge of the private key, by using the online tools on WIMS. You are tempted to do so.

Step 1. Compute the privatge key, that is, the integer such that *x*
is the inverse of *x*
in
. (Among the choices of , you should take the smallest positive integer.)

Yes, .

Step 2. Now you have intercepted the following crypted message (number). What is the original message (number)? (This must be a number between 0 and *N*-1.)

Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

- Description: collection of exercises on the RSA cryptosystem. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
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