Private Key Generation

RSA algorithm is the abbreviation of Rivest-Shamir-Adleman Algorithm and it deals with public key encryption and decryption of messages. The idea behind this algorithm is that , it is easy to multiply two very large prime numbers but it is a herculian task to factorize this product and trace back its original factors. This led to the idea of having 2 keys, one public and the other one private. The public key is available to everyone and it is used to encypt and send a secure message across the channel. This Cipher text can only be decrypted by using the private key, only available with the intendent receiver.

This started as a lab assignment for my cryptology class, but has since interested me to learn more about public key cryptography. The first task in my lab assignment was to generate a private key when the prime numbers and the public key are known. BIGNUM has been used in these assignments in order to escape the constraint of being able to use numbers that are at max. 64 bits long.

For the below example, the prime numbers and the exponent are:
p= F7E75FDC469067FFDC4E847C51F452DF
q=E85CED54AF57E53E092113E62F436F4F
e=0D88C3


The above picture gives us the code for private key generation.


This picture is the snippet of the output screen displaying the private key value for the above mentioned public keys and prime numbers.

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