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- Rsa Key Generation Algorithm
Nov 04, 2014 The RSA Encryption Algorithm (1 of 2: Computing an Example) - Duration: 8:40. Eddie Woo 400,470 views. Dec 28, 2019 For example, the cryptography package includes a RSA decryption example, which uses an existing privatekey variable to decrypt ciphertext, given (in addition to the ciphertext) a padding configuration. The latter is necessary because there are multiple ways you can pad out encrypted data to fixed-length blocks. New in version 0.5. Generates a new RSA private key using the provided backend. Keysize describes how many bits long the key should be. Larger keys provide more security; currently 1024 and below are considered breakable while 2048 or 4096 are reasonable default key sizes for new keys.
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In this chapter, we will focus on step wise implementation of RSA algorithm using Python.
Generating RSA keys
The following steps are involved in generating RSA keys −
- Create two large prime numbers namely p and q. The product of these numbers will be called n, where n= p*q
- Generate a random number which is relatively prime with (p-1) and (q-1). Let the number be called as e.
- Calculate the modular inverse of e. The calculated inverse will be called as d.
Algorithms for generating RSA keys
We need two primary algorithms for generating RSA keys using Python − Cryptomath module and Rabin Miller module.
Cryptomath Module
The source code of cryptomath module which follows all the basic implementation of RSA algorithm is as follows −
RabinMiller Module
The source code of RabinMiller module which follows all the basic implementation of RSA algorithm is as follows −
The complete code for generating RSA keys is as follows −
Output
The public key and private keys are generated and saved in the respective files as shown in the following output.
Now let's demonstrate how the RSA algorithms works by a simple example in Python. The below code will generate random RSA key-pair, will encrypt a short message and will decrypt it back to its original form, using the RSA-OAEP padding scheme.
First, install the
pycryptodome
package, which is a powerful Python library of low-level cryptographic primitives (hashes, MAC codes, key-derivation, symmetric and asymmetric ciphers, digital signatures):RSA Key Generation
Now, let's write the Python code. First, generate the RSA keys (1024-bit) and print them on the console (as hex numbers and in the PKCS#8 PEM ASN.1 format):
Run the above code example: https://repl.it/@nakov/RSA-Key-Generation-in-Python.
We use short key length to keep the sample input short, but in a real world scenario it is recommended to use 3072-bit or 4096-bit keys.
RSA Encryption
Next, encrypt the message using RSA-OAEP encryption scheme (RSA with PKCS#1 OAEP padding) with the RSA public key:
Run the above code example: https://repl.it/@nakov/RSA-encryption-in-Python.
RSA Decryption
Rsa Key Generation Example Python Free
Finally, decrypt the message using using RSA-OAEP with the RSA private key:
Run the above code example: https://repl.it/@nakov/RSA-decryption-in-Python.
Sample Output
A sample output of the code execution for the entire example is given below:
Notes:
Rsa Key Generation Example Python Pdf
- If you run the above example, your output will be different, because it generates different random RSA key-pair at each execution.
- Even if you encrypt the same message several times with the same public key, you will get different output. This is because the OAEP padding algorithm injects some randomness with the padding.
- If you try to encrypt larger messages, you will get and exception, because the 1024-bit key limits the maximum message length.
Rsa Key Generation Algorithm
Now play with the above code, modify it and run it to learn how RSA works in action.