Why does RSA need prime numbers?

The reason prime numbers are fundamental to RSA encryption is because when you multiply two together, the result is a number that can only be broken down into those primes (and itself an 1). It’s easy enough to break 187 down into its primes because they’re so small.

What is P and q in RSA?

RSA in Practice Note that both the public and private keys contain the important number n = p * q . The security of the system relies on the fact that n is hard to factor — that is, given a large number (even one which is known to have only two prime factors) there is no easy way to discover what they are.

Can P and q be equal in RSA?

When using RSA cryptography, it is possible to have the decrypted message and the initial message the same when p and q are the same.

Why is q not a prime number?

From the form of the number Q, it is obvious that no integer from 2 to P divides evenly into Q, because each division would leave a remainder of 1. If Q is not prime, it must be evenly divisible by some prime larger than P. On the other hand, if Q is prime, Q is itself a prime larger than P.

Why is prime number so important?

Most modern computer cryptography works by using the prime factors of large numbers. Primes are of the utmost importance to number theorists because they are the building blocks of whole numbers, and important to the world because their odd mathematical properties make them perfect for our current uses.

How does RSA work simple?

An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone, via the public key, but can only be decoded by someone who knows the prime numbers. Breaking RSA encryption is known as the RSA problem.

How do I choose RSA primes?

Preselect a random number with the desired bit-size. Ensure the chosen number is not divisible by the first few hundred primes (these are pre-generated) Apply a certain number of Rabin Miller Primality Test iterations, based on acceptable error rate, to get a number which is probably a prime.