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## RSA Algorithm with Example | Asymmetric Key Cryptography (Public Key Cryptography)

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As we all know that there are two types of Cryptography present in the field of security i.e. Symmetric and Asymmetric key cryptography. So AES and DES Symmetric cryptography methods we have already seen in the previous posts. Now in this post, we will explore the RSA algorithm in detail which is basically the foundation stone for the RSA Asymmetric cryptography process. Further, we will also look into an example of the RSA algorithm application to make the topic simpler . First, we should recap the basics discussed earlier, there are total of three types of the key present in the cryptography method . These are mainly secret key , public key and private key . Out of these secret keys is used for the Symmetric cryptography process, whereas the other two i.e. public and private keys are used for the Asymmetric cryptography. Public key algorithms also called asymmetric key algorithms. Two different keys are used during the encryption and decryption process (one key for encryption and second key used at the time of decryption). RSA algorithm is the best example of asymmetric key cryptography. The private key (only known to the owner) & Public key (possibly known to everyone) in the Asymmetric cryptography .

**What Is The RSA Algorithm In Asymmetric Key Cryptography ?**

The most common public key algorithm is RSA . Ron Rivest, Adi Shamir and Len Aldeman have developed this algorithm (RivestShamir-Aldeman) in 1978. It is a public-key encryption algorithm. It is a block-cipher that converts plain text into cipher text at the sender se and vice versa at the receiver se. The algorithm works as follows : Note : In the below steps the symbol ‘^’ represents raised to values for e.g. if 2^2 given that means 2 raised to the power 2 which is 4 1. Select two prime numbers a and b where a is not equal to b. 2. Calculate n = a * b 3. Calculate Φ(n) = (a-1) * (b- 1). 4. Select e such that, e is relatively prime to Φ(n) i.e. gcd (e, Φ(n)) = 1 and 1 < e < Φ(n). 5. Calculate of such that d = e^(-1) mod Φ(n) or ed mod Φ(n) = 1. 6. Public key = {e,n}, private key = {d,n). 7. Find out ciphertext using the formula. C = P^e mod n where, P < n and C = Ciphertext, P = Plaintext, e = Encryption key and n = Block size. 8. P = C^d mod n Plaintext P can be obtain using the given above formula (step 8). Where, d = decryption key. Both sender and receiver know the value of n. In addition, the sender must know encryption key ‘e’ and receiver must know decryption key ‘d’.

**RSA Algorithm Example In Reality !!**

Now its time for its application so that you can understand this concept in a well-applied manner indeed . Let us now Calculate cipher text using RSA algorithm given data as follows: Prime numbers p, q as 7, 17 respectively and plain text message is to be sent is 10. By using RSA algorithm as mentioned above [Refer the RSA algorithm above] Step 1 : Prime numbers are 7 and 17 i.e. a = 7, b=17 Step 2 : value of n = a*b = 7 * 17 = 119. Step 3 : Φ(n) = (a-1) * (b-1) = (7-1) * (17-1) = 6* 16 = 96 Step 4 : Select e such that it is relatively prime to Φ(n) i.e. gcd(e, Φ(n)) = 1 If we select e as 3 then it is not relatively prime p 96 because e =1*3 and 96 =2*2*2*2*2*3 (gcd must be 1) Hence , we select e as 5 (gcd must be 1) Thus , e = 1*5 gcd (5, 96) = 1 Hence e = 5 (encryption key) Step 5 : Now we have to calculate d such that d = e^(-1) mod Φ(n) Hence , e * d mod Φ(n) = 1 , i.e. 5 * d mod 96 = 1 Now using RSA algorithm we can compute the following : d = ((Φ(n) * i) + 1 )/5 where i = 1 to 9 So just put the value of i as 1 to 9 and check the value at which the value of d is a perfect integer i.e. d must be completely divisible by ‘e’. d = ((96 * 1)+ 1 ) / 5 = 19.4 d = ((96*2)+1) / 5 = 38.6 , d = ((96*3) +1)/ 5 = 57.8 d = ((96*4)+1) / 5 = 77 So at i = 4 we got value of d as perfect integer . Hence d = 77 (decryption key) Step 6 : Now the Public key = (e, n) = (5, 119) And , the Private key = [d, n] = (77, 119) Step 7 : Calculate cipher text message for given plain text message m = 10. Plain text denoted as p = 10 (m denoted as p) C = P^e mod n = 10^5 mod 119 (value of e calculated above) It can be represented as = 10^5 mod 119 = [1000 mod 119] *[100 mod 119] mod 119 100^5 mod 119 = [10^3 mod 119] *[10^2 mod 119] mod 119 C = P^e mod n = 100000 mod 119 = 40 Step 8 : Now calculate plain text P required at the time of decryption. Once sender sends 40 to the receiver then receiver can calculate plain text p. P = C^d mod n = 40^77 mod 119 Now represent 40^77 mod 119 as mention above it will results p as 10. Because decryption process always yields original message (plain text) P = 40^77 mod 119 = 10 Thus we successfully able to decrypt the original plain text as given initially by the sender using the RSA algorithm

**Limitations Of RSA Method **

Although RSA can be used to encrypt and decrypt actual messages, it is very slow if the message is long. RSA, therefore, is useful for short messages such as a small message digest or a symmetric key to be used for a symmetric-key cryptosystem.

**Possible Attacks In RSA Method Of Cryptograthy !!**

Although RSA is a mush secure encryption method, still some attacks are possible : Brute force attack : Hacker tries all possible private keys. Mathematical attacks : Hackers attacks on n i.e. tries to factorize the product of two prime numbers. Tuning attacks : It totally depends on the running time of the decryption algorithm. Chosen Cipher text attack : Hacker tries to attack the properties of RSA algorithm RSA process is very wely used for the digital signature based authentications. Hope you really liked this post. Stay tuned for more interesting stuff in this series . report this ad

## What is RSA algorithm with example?

RSA algorithm is **a public key encryption technique** and is considered as the most secure way of encryption. It was invented by Rivest, Shamir and Adleman in year 1978 and hence name RSA algorithm.

## Which is an example of an RSA?

RSA is an example of public-key cryptography, which is illustrated by the following example: **Suppose Alice wishes to send Bob a valuable diamond, but the jewel will be stolen if sent unsecured.**

## What are examples of asymmetric key algorithms?

…

Difference Between Symmetric and Asymmetric Key Encryption.

Symmetric Key Encryption | Asymmetric Key Encryption |
---|---|

Examples: 3DES, AES, DES and RC4 | Examples: Diffie-Hellman, ECC, El Gamal, DSA and RSA |

## What is RSA encryption algorithm?

The RSA algorithm is **an asymmetric cryptography algorithm**; this means that it uses a public key and a private key (i.e two different, mathematically linked keys). As their names suggest, a public key is shared publicly, while a private key is secret and must not be shared with anyone.

## Where is RSA algorithm used?

RSA is still seen in a range of **web browsers, email, VPNs, chat and other communication channels**. RSA is also often used to make secure connections between VPN clients and VPN servers. Under protocols like OpenVPN, TLS handshakes can use the RSA algorithm to exchange keys and establish a secure channel.

## Is RSA symmetric or asymmetric?

RSA is named for the MIT scientists (Rivest, Shamir, and Adleman) who first described it in 1977. It is an **asymmetric** algorithm that uses a publicly known key for encryption, but requires a different key, known only to the intended recipient, for decryption.

## How is RSA algorithm implemented?

**Implementation of RSA Algorithm:**

- Consider two prime numbers p and q.
- Compute n = p*q.
- Compute ϕ(n) = (p – 1) * (q – 1)
- Choose e such gcd(e , ϕ(n) ) = 1.
- Calculate d such e*d mod ϕ(n) = 1.
- Public Key {e,n} Private Key {d,n}
- Cipher text C = Pe mod n where P = plaintext.

## How RSA works step by step?

**Steps in RSA Algorithm**

- Choose two large prime numbers (p and q)
- Calculate n = p*q and z = (p-1)(q-1)
- Choose a number e where 1 < e < z.
- Calculate d = e-1mod(p-1)(q-1)
- You can bundle private key pair as (n,d)
- You can bundle public key pair as (n,e)

## Which key is used for asymmetric encryption?

Asymmetric encryption uses a mathematically related pair of keys for encryption and decryption: **a public key and a private key**. If the public key is used for encryption, then the related private key is used for decryption. If the private key is used for encryption, then the related public key is used for decryption.

## What are asymmetric encryption algorithms?

Asymmetric-key algorithms are commonly referred to as “**public-key algorithms**”. They use two mathematically associated keys knows as public and private keys. One key is used for data encryption, and the other is used for decryption of data.

## Which algorithm is not used in asymmetric-key cryptography?

Which one of the following algorithm is not used in asymmetric-key cryptography? Explanation: **Electronic code book algorithm** is a block cipher method in which each block of text in an encrypted message corresponds to a block of data. It is not feasible for block sizes smaller than 40 bits.

## Which choices are examples of asymmetric encryption?

**Examples of asymmetric encryption include:**

- Rivest Shamir Adleman (RSA)
- the Digital Signature Standard (DSS), which incorporates the Digital Signature Algorithm (DSA)
- Elliptical Curve Cryptography (ECC)
- the Diffie-Hellman exchange method.
- TLS/SSL protocol.

## Why RSA algorithm is secure?

At the most basic level, RSA public keys are the result of two large, randomly generated prime factors. They’re created using random number generators. This means that **the entire security premise of the RSA algorithm is based on using prime factorization as a method of one way encryption**.

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### Public Key Cryptography with RSA Algorithm – Naukri Learning

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### Public Key Cryptography | RSA Algorithm Example – Gate …

In the RSA public key cryptosystem, the private and public keys are (e, n) and (d, n) respectively, where n = p x q and p and q are large primes. Beses, n is …

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