RSA_Algorithm encrypt password RSA(Rivest-Shamir-Adleman) is a public-key cryptosystem that is widely used for security transmission. RSA key generation Algorithm1 (pseudo code) input: Security parameter l 1.Randomly select two primes p and q of the same bitlength l/2. 2.Compute n = p * q, and θ = (p - 1) * (q - 1). 3.Select an arbitrary integer e with 1 < e < θ and gcd(e, θ) = 1 4.Compute the integer d satisfying 1 < d < θ and ed ≡ 1 (modθ). 5.return (n, e, d)
RSA encryption and signature schemes use the fact that m^(ed) ≡ m (mod n) //Please learn the modulo theory
The encryption and decryption procedures for the (basic) RSA public-key encryption scheme are presented as Algorithms2 and 3. Decryption works because c^d ≡ (m^e)^d ≡ m (mod n) The security relies on the difficulty of computing the plaintext m from the ciphertext c = m^e mod n and the public parameters n and e. This is the problem of finding eth roots modulo n and is assumed(but has not been proven) to be as difficult as the integer factorization problem.
Algorithm2 (pseudo code) RSA encryption input: plaintext m in [0, n - 1]. 1.Ciphertext c 2.Compute c = m^e mod n 3.return c
Algorithm3(pseudo code)RSA decryption input: RSA public key(n, e) RSA private key d, ciphertext c 1.Plaintext m 2.Compute m = c^d mod n 3.return m
[1] Darrel Hankerson Alfred Menezes Scott Vanstone Guide to EllipticCurve Cryptography