Rsa Algorithm
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The RSA algorithm document describes the steps to generate a public/private key pair for encryption and decryption. It involves selecting two large prime numbers p and q, computing n as their product, and using n along with the prime factors to calculate the private key exponent d that corresponds to the public key exponent e, such that ed = 1 mod φ(n). The example demonstrates computing the values for a specific case where p=3 and q=11. The Diffie-Hellman key exchange document describes a protocol where Alice and Bob can establish a shared secret key over an insecure channel. It involves Alice generating a public value gx mod p and Bob generating a public value gy mod p, then each uses the other
Rsa Algorithm
- 1. RSA Algorithm: 1. Select two very large prime numbers. 2. n = p.q 3. ɸ = (p - 1).(q - 1) 4. Select e; such that, e is relatively prime to ɸ and e < ɸ, gcd (e, ɸ) = 1 5. Select d; such that, d.e mod ɸ = 1 or e = 1 mod ɸ 6. Public key : {e, n} Private key : {d, n} 7. e = pe mod n p = cd mod n Example: 1. p = 3, q = 11 2. n = 3 x 11 = 33 3. ɸ = (3 – 1).(11 – 1) = 2 x 10 = 20 4. e = 3, 7, 9, 11, 13, 17, 19 d = 1, 3 mod 20 ≠ 1 5. d = 7, d.e mod 20 = 1 d = 2, 6 mod 20 ≠ 1 d.3 mod 20 = 1 d = 3, 9 mod 20 ≠ 1 d = 4, 12 mod 20 ≠ 1 8. Public key : {33, 33} d = 5, 15 mod 20 ≠ 1 d = 6, 18 mod 20 ≠ 1 Private key : {7, 33} d = 7, 21 mod 20 = 1
- 2. Diffe-Hellman Protocol: k = gxy mod p Alice Bob R1 gx mod p R2 gy mod p R R k = R2x mod p k = R1y mod p = (gy mod p)x mod p = (gx mod p)y mod p = gxy mod p = gxy mod p k is the shared key p and g : two large number with some properties.