M3: Encryption r By Andrew Stringer

What is it? Encryption: A way of converting data(text, film and images) into something which makes no sense unless you have a key. 2

Why encrypt and decrypt? Text can be encrypted, to make sure the privacy of the data sent over a network between a two devices stays secure. Cryptography - The methods to encrypt text. Cryptanalysis - How to decode an encrypted text. Conventional or single key encryption - a simple algorithm is used to transform the text Substitution cipher - each letter of the alphabet is substituted with a different letter or symbol. (e.g., A=1, B=2) Ceasar's method - replace every letter in the alphabet with the letter 3 away (E.g., A=D, B=E, C=F, D=G, E=H, etc…) 3

Encryption And Decryption Other way of substituting data is to plan random substitutions, so they are a bit harder to crack. The sender uses the encryption to encrypt the message The sender transmits the message to the receiver The receiver decodes the message How does this become decrypted? Q:How can this be done securely so that no one else can decode the message? A: The sender needs to send the key to the receiver. For example: When purchasing from the wbes, the buyer’s workstation must encrypt the data before it sends it over the Internet to the seller’s server 4

Encryption Most methods of encrypting use mathematical formulas and have a key to encode the data The encryption key is a very large number (1024 bit value). The longer the number the harder is it to crack. 5

Encryption And Decryption Symmetric/ Private Key Encryption DES (Data Encryption Standard) is very commonly used Because each sender and receiver needs a different key, this encryption is very secure and is used by governments. It is rarely used for e-commerce transactions over the Internet This type encryption requires a secure way to receive the key to both devices 6

Encryption And Decryption Asymmetric / Public Key Encryption Uses two numeric keys The public key is available to anyone wishing to communicate securely with the key’s owner, the private key is available only to the owner (have mentioned this in P3) Anyone who has a public key can encrypt information. however, cannot decrypt it. A new key is sent to the device requires the private key so it can be decrypted. 7

Example of Asymmetric Encryption Choose two large prime numbers, p and q and compute N = p * q and x = (p-1)*(q-1) Choose a number relatively prime to x and call it e. This means that e is not a prime factor of x or a multiple of it. Find d such that e * d = 1 mod x. To encrypt: Cipher = Plaintexte (mod n) To decrypt: Plaintext = Cipherd (mod n) Choose p = 7 and q = 13 We then calculate N = 7∗13 = 91 and x=(p−1)(q−1) = 72 We next select ke relatively prime to 72 and< 72, yielding 5 Finally,we calculate kd such that kekd mod 72 = 1, yielding 29 public key (ke, N) = (5, 91) and private key (kd ,N) = (29, 91) 32 codes in 2: 325= 2 (mod 91) 2 decodes into 32: 229=32 (mod 91) 8