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In a system an RSA algorithm with p = 5 and q = 11, is implemented for data security. What is the value of the decryption key if the value of the encryption key is 27 ?

In a system an RSA algorithm with p = 5 and q = 11, is implemented for data security. What is the value of the decryption key if the value of the encryption key is 27 ? Correct Answer 3

The correct answer is “option 1”.

CONCEPT:

RSA algorithm (Rivest-Shamir-Adleman) is an algorithm used by modern technologies to encrypt and decrypt messages.

It is asymmetric or public-key cryptography that uses two keys for encryption & decryption: Public key and private key.

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Steps for RSA algorithm:

1. Choose two large prime numbers P & Q.

2. Find the product of chosen two numbers, N = P × Q

3. Calculate Euler’s totient (Φ) = (P - 1)(Q - 1)

4. Choose random integer e (public key) such that,

d x e = 1(mod Φ)

Where,

d is the private key.

6. Calculate Ciphertext C = mod n.

7. Calculate Plain text P = mod n.

CALCULATION:

Given two prime numbers are p = 5, q = 11

Product, n = 5 × 11 = 55

Φ = (5 - 1) × (11 - 1) = 40

e = 27,

d x 27 = 1 (mod 40)

d = 3

Hence, the correct answer is “option 1”.

Related Questions

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