rsa decrypt algorithm python implementation

gcd ( e, phi ) = 1 : break d = multiplicative_inverse ( e, phi ) return ( n, e, d ) def rsa_encrypt ( message, n, e ): return modular. getrandbits ( bits ) | 1 0 : if m % 2 = 1 : a = ( a * x ) % n x = ( x * x ) % n m //= 2 return a def extended_gcd ( a, b ): '''Returns pair (x, y) such that xa + yb = gcd(a, b)''' x, lastx, y, lasty = 0, 1, 1, 0 while b != 0 : q, r = divmod ( a, b ) a, b = b, r x, lastx = lastx - q * x, x y, lasty = lasty - q * y, y return lastx, lasty def multiplicative_inverse ( e, n ): '''Find the multiplicative inverse of e mod n.''' x, y = extended_gcd ( e, n ) if x < 0 : return n + x return x def rsa_generate_key ( bits ): p = generate_random_prime ( bits / 2 ) q = generate_random_prime ( bits / 2 ) # Ensure q != p, though for large values of bits this is # statistically very unlikely while q = p : q = generate_random_prime ( bits / 2 ) n = p * q phi = ( p - 1 ) * ( q - 1 ) # Here we pick a random e, but a fixed value for e can also be used. Then implement the RSA algorithm using the steps mentioned aboveĭef generate_random_prime ( bits, primality_test ): '''Generate random prime number with n bits.''' get_random_t = lambda : random. We use the Rabin-Miller algorithms to check if the number is prime or not. Then we proceed to check t+it+i for primality starting from i=0i=0 and onwards. Given a, n and e, with 08 for all our intended purposes.

However, given n=pq,n=pq, it is difficult to factor out pp and q.q.

It is easy to multiply two large primes together, calculating n=pq.n=pq.

It is easy to find two distinct large primes pp and q.q.

The acronym RSA is made of the initial letters of the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman, who first publicly described the algorithm in 1978 In RSA, this asymmetry is based on the practical difficulty of the factorization of the product of two large prime numbers, the “factoring problem”. The encryption key is public and it is different from the decryption key which is kept secret (private). RSA (Rivest–Shamir–Adleman) is one of the first public-key cryptosystems.

This is a explanation of RSA encryption, along with a simple Python implementation of it.

Rsa decrypt algorithm python implementation