The RSA Adventure: The Power Of Prime

Why is RSA cryptosystem comparatively more secure than other systems?

A fortress would appear to be a playpen in comparison to the RSA cryptosystem's level of security. It's similar to having a closed-door club where the only people who know the secret handshake can enter. But the RSA cryptosystem is accessible to everyone, unlike those closed-door groups (who knows the secret).

Think about sending your best friend a private message that you don't want your nosy neighbor to see. It could be programmed, but that wouldn't be particularly secure. Instead, you encrypt your message using the RSA cryptosystem. It's similar to wrapping your message in several layers of protective paper and tying a strong ribbon around a gift.

The RSA cryptosystem is an asymmetric algorithm that uses two keys - a public key and a private key. The public key is like the address to your secret club, it's available for everyone to see. But the private key is like the secret handshake, only you and your friend know it. So when you send your message to your friend, it's encrypted with their public key. Only they can decrypt it with their private key. It's like sending a present to your friend, they're the only ones who can unwrap it and see what's inside.

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Now, let's talk about the nosy neighbor. They see your message, they know it's encrypted, but they can't read it. It's like trying to unwrap a present that's not for you, but you can't because you don't know the secret. The RSA cryptosystem is so secure, even a super computer would take billions of years to crack it.

A quick instance of the RSA algorithm

Let us bring our favorite's  Alice and Bob to understand this cryptosystem better

Let's say Alice wishes to send Bob a covert message. They both agree to safeguard their communication using the RSA cryptosystem

Choose the two significant prime numbers x and y. It is necessary for the prime numbers to be large in order to make them challenging to decipher.

1.To calculate n

n=x*y   (assume x=3, y=11)

2.Calculate totient function,

 t =(x-1)(y-1) = 2*10 =20

3.Select an integer e that is co-prime to the totient function such that 

1< e < t   (assume e=7)

The pair of numbers (n,e) makes up the public key.

4.To find the private key d,

d=1 mod t

Hence Bob's public key is (e=7, n=33). And his private key is (n=33,d=3).

"HI BOB" is the message to be delivered to Bob. Alice turns each letter into its corresponding ASCII code. The text changes to 72 73 66 79 66.

Each number is raised to the power of 7 by Alice, who then divides the result by 33 to get the remaining number. The message is then translated as:

CIPHERTEXT= (72^7 mod 33), (73^7 mod 33), 
            (66^7 mod 33), (79^7 mod 33), (66^7 mod 33) 

           = 17, 31, 30, 13, 30

Bob receives the encrypted message and uses his private key (d=3) to decrypt it. He raises each number in the encrypted message to the power of 3 and takes the remainder when divided by 33. The decrypted message becomes:

PLAINTEXT = (17^3 mod 33), (31^3 mod 33), 
            (30^3 mod 33), (13^3 mod 33), (30^3 mod 33) 

                        = 72, 73, 66, 79, 66

The initial message is revealed when Bob changes the digits back into letters: "HI BOB."

To summarize the above steps -

Bob produces two keys—a public key and a private key—a pair of them. He sends Alice his public key.

Alice encrypts her message with Bob's public key using this method. She then delivers Bob the encrypted communication.

Bob uses his private key to decrypt the communication after it has been encrypted. Now he can read the original message Alice sent.

Where RSA is used in real life?

  1. Secure Web Browsing: RSA is frequently used to protect internet communications, including HTTPS-secured web browsing.
  2. Email Security: Email messages and digital signatures are encrypted using RSA to safeguard email conversations.
  3. RSA is used to establish digital signatures, which are needed to confirm the legitimacy of electronic documents.
  4. Virtual private networks (VPNs): RSA is used to protect VPN connections and offer secure remote access to network resources.
  5. File and Disk Encryption: RSA is used to encrypt files and disc partitions, shielding private information from prying eyes.
  6. Software protection: RSA is used to safeguard software and thwart illegal usage, tampering, and reverse engineering.
  7. Financial Transactions: Online payment systems, e-commerce, and banking all employ RSA to secure financial transactions.
  8. Smart Cards: RSA is used to protect sensitive data, including credit card numbers, personal identifying information, and other data, contained on smart cards.

In Conclusion:

Finally, it should be noted that the RSA cryptosystem is a well-known and incredibly safe technique for sending sensitive data over the internet and other networks. The use of public and private key encryption, which makes sure that only the intended receiver may access the encrypted information, is its strongest point. RSA continues to be one of the most significant and trustworthy techniques for secure data transmission due to its extensive use and successful track record. The RSA cryptosystem continues to be essential in ensuring the security of our digital information, whether it is used for safe online browsing, email, digital signatures, VPNs, or financial transactions.