1. Asymmetric encryption

2. Asymmetric encryption, often called "public key" encryption, allows Alice to send Bob an encrypted message without a shared secret key there is a secret key, but only Bob knows what it is, and he does not share it with anyone, including Alice

3. Asymmetric encryption

4. Bob creates a pair of keys, one of which he keeps secret and one of which he sends to Alice. Alice composes a confidential message and encrypts it using the key that Bob has sent to her. Alice sends the encrypted data to Bob. Bob uses his secret key to decrypt the data and reads the confidential message.

5. Asymmetric encryption Asymmetric algorithms include a "key generation" protocol that Bob uses to create his key pair, as shown by Figure 15-2. Following the protocol results in the creation of a pair of keys that have a mathematical relationshipthe exact detail of the protocol and the relationship between the keys is different for each algorithm.

6. Asymmetric encryption

7. Creating Asymmetric Keys using RSA Algorithm each user generates a public/private key pair by: selecting two large primes at random - p, q computing their system modulus N=p.q – note ø(N)=(p-1)(q-1) selecting at random the encryption key e where 1< e<ø(N), gcd(e,ø(N))=1 solve following equation to find decryption key d – e.d=1 mod ø(N) and 0≤d≤N Or d = e -1 (mod ( (n)) publish their public encryption key: KU={e,N} keep secret private decryption key: KR={d,p,q}

8. Example of RSA Ciphertext C = M e mod n Plaintext M = C d mod n Example: p = 17, q = 11 n = 178 ø(N) = 160 e = 7 D = 23 PU = { 7, 187 } ; PR = { 23, 187 } M= 88; C =88 7 mod 187 = 11 C = 11 23 mod 187 = 88

9. Encryption

10. Decryption

11. Solve this example Start with p= 61 q=53