The RSA algorithm is an asymmetric cryptographic algorithm used for public-key encryption and digital signatures. It uses two different keys - a public key can be shared publicly, and a private key must be kept secret. The security of RSA is based on the difficulty of factoring large prime numbers. RSA allows a client to securely send encrypted data to a server, which can only be decrypted by someone with the corresponding private key.

1. RSA algorithm (Rivest-Shamir-Adleman)
By
Manish Kumar Giri

2. - RSA (Rivest–Shamir–Adleman) is an algorithm used by modern
computers to encrypt and decrypt messages.
- It is an asymmetric cryptographic algorithm.
- Asymmetric means that there are two different keys.
- This is also called public key cryptography, because one of the keys
can be given to anyone. he other key must be kept private.
- The algorithm is based on the fact that finding the factors of a large
composite number is difficult: when the factors are prime numbers,
the problem is called prime factorization.
- It is also a key pair (public and private key) generator
RSA algorithm (Rivest-Shamir-Adleman)

3. How RSA Encryption Algorithm works

4. How RSA Algorithm works?

5. Idea behind RSA algorithm
- The idea of RSA is based on the fact that it is difficult to factorize
a large integer.
- The public key consists of two numbers where one number is
multiplication of two large prime numbers.
- Private key is also derived from the same two prime numbers.
- So if somebody can factorize the large number, the private key is
compromised.
- Therefore encryption strength totally lies on the key size and if
we double or triple the key size, the strength of encryption
increases exponentially.
- RSA keys can be typically 1024 or 2048 bits long, but experts
believe that 1024 bit keys could be broken in the near future. But
till now it seems to be an infeasible task.

6. RSA
workflow

7. RSA Algorithm

8. RSA algorithm (Rivest-Shamir-Adleman)
- Asymmetric actually means that it works on two different keys i.e.
Public Key and Private Key. As the name describes that the Public
Key is given to everyone and Private key is kept private.
- An example of asymmetric cryptography :
1. A client (for example browser) sends its public key to the server
and requests for some data.
2. The server encrypts the data using client’s public key and sends
the encrypted data.
3. Client receives this data and decrypts it.

9. RSA algorithm (Rivest-Shamir-Adleman)

10. RSA algorithm

11. RSA Example

12. RSA Example

13. Attacks against plain RSA
There are a number of attacks against plain RSA as described below.
1. When encrypting with low encryption exponents (e.g., e = 3) and small values of
the m, (i.e., m < n1/e) the result of me is strictly less than the modulus n. In this
case, ciphertexts can be easily decrypted by taking the eth root of the
ciphertext over the integers.
1. If the same clear text message is sent to e or more recipients in an encrypted
way, and the receivers share the same exponent e, but different p, q, and
therefore n, then it is easy to decrypt the original clear text message via the
Chinese remainder theorem. Johan Håstad noticed that this attack is possible
even if the cleartexts are not equal, but the attacker knows a linear relation
between them.This attack was later improved by Don Coppersmith.

14. Attacks against plain RSA
- Because RSA encryption is a deterministic encryption algorithm (i.e., has no
random component) an attacker can successfully launch a chosen
plaintext attack against the cryptosystem, by encrypting likely plaintexts
under the public key and test if they are equal to the ciphertext.
- A cryptosystem is called semantically secure if an attacker cannot
distinguish two encryptions from each other, even if the attacker knows (or
has chosen) the corresponding plaintexts.
- RSA without padding is not semantically secure

15. Advantages of RSA
The advantages includes
1. RSA algorithm is safe and secure for its users through the use of
complex mathematics.
1. RSA algorithm is hard to crack since it involves factorization of
prime numbers which are difficult to factorize. Moreover,
1. RSA algorithm uses the public key to encrypt data and the key is
known to everyone, therefore, it is easy to share the public key.

16. Disavantages of RSA
The disadvantages includes
1. RSA algorithm can be very slow in cases where large data needs to
be encrypted by the same computer. It requires a third party to
verify the reliability of public keys.
1. Data transferred through RSA algorithm could be compromised
through middlemen who might temper with the public key system.
1. In conclusion, both the symmetric encryption technique and the
asymmetric encryption technique are important in encryption of
sensitive data.

17. - https://www.geeksforgeeks.org/rsa-algorithm-cryptography/
- https://searchsecurity.techtarget.com/definition/RSA
- https://simple.wikipedia.org/wiki/RSA_algorithm
- https://www.google.com/search?q=rsa+algorithm&tbm=isch&ved=2ahUKEwj5-
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References

18. Thank You