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How to solve RSA Algorithm Problems?
• Last Updated : 19 Feb, 2020

RSA algorithm is an asymmetric cryptography algorithm which means, there should be two keys involve while communicating, i.e., public key and private key. There are simple steps to solve problems on the RSA Algorithm.

Example-1:

• Step-1: Choose two prime number and Lets take and • Step-2: Compute the value of and It is given as, and Here in the example,  • Step-3: Find the value of (public key)
Choose , such that should be co-prime. Co-prime means it should not multiply by factors of and also not divide by Factors of are, so should not multiply by and and should not divide by 20.

So, primes are 3, 7, 11, 17, 19…, as 3 and 11 are taken choose as 7

Therefore, • Step-4: Compute the value of (private key)
The condition is given as, where y is the value of .

To compute the value of ,

1. Form a table with four columns i.e., a, b, d, and k.
2. Initialize a = 1, b = 0, d = , k = – in first row.
3. Initialize a = 0, b = 1, d = , in second row.
4. From the next row, apply following formulas to find the value of next a, b, d, and k, which is given as
• • • • As soon as, , stop the process and check for the below condition

if  if  For a given example, the table will be,

abdk
1020
0172
1-261
-131

As in the above table , stop the process and check for the condition given for the  To verify that is correct, the above condition should satisfy, i.e. . Hence is correct.

• Step-5: Do the encryption and decryption
Encryption is given as, Decryption is given as, For the given example, suppose , so
Encryption is Decryption is Therefore in the final, , , , , and Example-2: GATE CS-2017 (Set 1)
In an RSA cryptosystem, a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of A is 35. Then the private key of A is?

1. and 2. Compute and 3. (public key)
4. Compute (private key)
abdk
10192
01355
1-5172
-2111 (private key)

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