Asymmetric encryption Asymmetric encryption Asymmetric encryption often called
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![Asymmetric encryption • Asymmetric encryption, often called "public key" encryption, allows Alice to send Asymmetric encryption • Asymmetric encryption, often called "public key" encryption, allows Alice to send](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-2.jpg)
![Asymmetric encryption Asymmetric encryption](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-3.jpg)
![Asymmetric encryption • Bob creates a pair of keys, one of which he keeps Asymmetric encryption • Bob creates a pair of keys, one of which he keeps](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-4.jpg)
![Asymmetric encryption • Asymmetric algorithms include a "key generation" protocol that Bob uses to Asymmetric encryption • Asymmetric algorithms include a "key generation" protocol that Bob uses to](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-5.jpg)
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![Creating Asymmetric Keys using RSA Algorithm • each user generates a public/private key pair Creating Asymmetric Keys using RSA Algorithm • each user generates a public/private key pair](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-7.jpg)
![Example of RSA Ciphertext C = Me mod n Plaintext M = Cd mod Example of RSA Ciphertext C = Me mod n Plaintext M = Cd mod](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-8.jpg)
![Encryption Encryption](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-9.jpg)
![Decryption Decryption](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-10.jpg)
![Solve this example • Start with p= 61 q=53 Solve this example • Start with p= 61 q=53](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-11.jpg)
- Slides: 11
![Asymmetric encryption Asymmetric encryption](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-1.jpg)
Asymmetric encryption
![Asymmetric encryption Asymmetric encryption often called public key encryption allows Alice to send Asymmetric encryption • Asymmetric encryption, often called "public key" encryption, allows Alice to send](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-2.jpg)
Asymmetric encryption • 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
![Asymmetric encryption Asymmetric encryption](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-3.jpg)
Asymmetric encryption
![Asymmetric encryption Bob creates a pair of keys one of which he keeps Asymmetric encryption • Bob creates a pair of keys, one of which he keeps](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-4.jpg)
Asymmetric encryption • 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.
![Asymmetric encryption Asymmetric algorithms include a key generation protocol that Bob uses to Asymmetric encryption • Asymmetric algorithms include a "key generation" protocol that Bob uses to](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-5.jpg)
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.
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Asymmetric encryption
![Creating Asymmetric Keys using RSA Algorithm each user generates a publicprivate key pair Creating Asymmetric Keys using RSA Algorithm • each user generates a public/private key pair](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-7.jpg)
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}
![Example of RSA Ciphertext C Me mod n Plaintext M Cd mod Example of RSA Ciphertext C = Me mod n Plaintext M = Cd mod](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-8.jpg)
Example of RSA Ciphertext C = Me mod n Plaintext M = Cd 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 = 1123 mod 187 = 88
![Encryption Encryption](https://slidetodoc.com/presentation_image_h/0b8b53a3f9582cbf3a2a2636d72f28fd/image-9.jpg)
Encryption
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Decryption
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Solve this example • Start with p= 61 q=53
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