# RSA Calculator + Online Solver With Free Steps

The free **RSA Calculator** is a helpful tool that can be used to determine the key in data encryption problems. The **Key** is an essential element for encrypting data to make communication safe.

The **calculator** needs three inputs which include two prime numbers and a public key to determine the private key for the problem.

## What Is the RSA Calculator?

**The RSA Calculator is an online calculator that uses the RSA algorithm to calculate the private key in data encryption.**

**RSA** algorithm is widely used in the domains of **computer networking**, **cryptography**, and **network security**. RSA is one of the toughest algorithms since it demands a large of calculations. It can be **challenging** to deal with the RSA algorithm when the network has many nodes and devices. One has to perform the long process of calculations for each node separately.

That’s why we offer you this advanced **RSA Calculator** which finds the private key in less than a second. Thus it gives spares you from going through the laborious process.

## How To Use the RSA Calculator?

You can use the **RSA Calculator **by putting the required prime numbers and the public key in their fields.

You can follow the given instructions to get accurate results from the calculator.

### Step 1

First, enter the public key in the **E** box**. **

### Step 2

Then put the first prime number in the **P **box.

### Step 3

Now enter the second prime number in the **Q **box. These two prime numbers are usually large and can vary from one application to another.

### Step 4

In the end, click **Submit **to start the processing.

### Result

The solution to the problem is demonstrated in multiple steps. First, it provides the **input interpretation **which displays the general form by putting the input values in the expression used to calculate the private key.

Then it gives the **integer value** of the private key obtained after the calculations. The private key is denoted by the letter **d**.

Lastly, it visualizes the value of the private key as a point in a single plane. This kind of representation is known as a **number line**.

## How Does the RSA Calculator Work?

This calculator works on the** RSA algorithm **by finding the** private **key pair for the given values of the public key pair.

The RSA algorithm is an** asymmetric** cryptography algorithm and it forms the basis of this calculator. The conception of this calculator will be cleared when there is knowledge about asymmetric cryptography algorithms.

### Asymmetric Encryption

The asymmetric encryption algorithms work with the two different keys. The first is the **public key** and the second is the** private key**. The public key is used for the **encryption** of data while the private key is used for** decryption**.

The two keys belong to the **receiver **always. While using this algorithm there is no need to interchange any secret key between the sender and receiver. Therefore it reduces the chances of exploitation.

The concept of asymmetric encryption is clear, now there is a need to understand the RSA algorithm.

### What Is RSA Algorithm?

The RSA algorithm is an** asymmetric encryption **algorithm and is treated as the most secure way of encryption. It was developed by Ron Rivest, Adi Shamir, and Leonard Adleman in 1978.

This algorithm encrypts the data using the receiver’s **public** key and decrypts it using the receiver’s** private **key.

**Public key** encryption is different from symmetric-key encryption which uses the same private key for encryption and decryption of data.

Hence the public key encryption algorithms such as the RSA algorithm are convenient in scenarios where there is no chance of allotting the keys in advance.

### How Does the RSA Algorithm Work?

The RSA algorithm works by generating the **public** and **private** keys before executing the functions that produce plain text and cipher text. This algorithm includes the following steps, which are explained below.

#### Generating the RSA Modulus

The first step is to select the two large** prime** numbers name **p** and **q** and then calculate their product **N** such as **N = p x q**.

#### Find the Number(e)

Select an integer **e** that should be** co-prime **to **(p-1)(q-1),** greater than 1, and less than (p-1)(q-1).

#### Generating the Public Key

The pair of numbers **(n,e)** bundle as** RSA Public** key.

#### Generating the Private Key

Generating the Private key is the main aim of this calculator which is calculated from the numbers **p**, **q**, and **e** that are found in the previous steps. The formula to find it is given by:

\[d= (e)^{-1}(1)\,mod(p-1)(q-1)\]

The pair of numbers **(n,d)** make up an **RSA Private** key.

#### Data Encryption and Decryption

The generation of the keys leads to the encryption of data. When the sender sends the plain message to the receiver using the receiver’s public key (n,e), this algorithm **encrypts **the plain text and makes it a **cipher text** using the following relation:

\[C= P^e\, mod \, N\]

Where **P** is a plain text and **C** is a cipher text.

\[P= C^d \, mod \, N\]

## Solved Examples

Here are some solved examples using the **RSA Calculator**.

### Example 1

In an RSA cryptosystem, a particular node uses two prime numbers **p = 13** and **q = 17** to generate both keys. If the public key is **e = 35**, then find the private key **d**.

### Solution

The solution is given as follows:

#### Input Interpretation

The expression to find the parameter **‘d’ **is given below.

\[ 35^{-1} mod ((13 -1)(17 – 1)) = d \]

#### Result

The numerical value of the private key is given as:

**d = 11**

**Number Line**

Figure 1 shows the number line representation of the key.

### Example 2

Consider the network of two nodes with the following details. Find the **‘d’** parameter.

**p = 61, d = 53, e = 17**

### Solution

#### Input Interpretation

\[ 17^{-1} mod ((61 -1)(53 – 1)) = d \]

#### Result

** d = 2753**

**Number Line**

The number line representation can be seen in figure 2.

*All the Mathematical Images/Graphs are created using GeoGebra.*