Encryption
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The document discusses encryption methods, focusing on symmetric key cryptography, public key cryptography, and their applications. It explains various encryption standards such as DES and AES, and details the RSA algorithm for public key encryption, including key generation and the basis of its security. The text also highlights practical applications of these cryptographic methods in secure communication and digital signatures.
![8-11
Public Key Cryptography
symmetric key crypto
requires sender, receiver
know shared secret key
public key crypto
radically different
approach [Diffie-
Hellman76, RSA78]
sender, receiver do not
share secret key
public encryption key
known to all
private decryption key
known only to receiver](https://image.slidesharecdn.com/encryption-151016114129-lva1-app6892/85/Encryption-11-320.jpg)
Encryption
- 1. 8-1 Encryption Eng. Mahmoud Abdeen Mohammed
- 2. 8-2 Why encryption secure sender s secure receiver channel data, control messages data data sender receiver Intruder
- 3. 8-3 There are bad guys out there who can! eavesdrop: intercept messages actively insert messages into connection impersonation: can fake (spoof) source address in packet (or any field in packet) hijacking: “take over” ongoing connection by removing sender or receiver, inserting himself in place denial of service: prevent service from being used by others (e.g., by overloading resources)
- 4. 8-4 The language of cryptography m plaintext message KA(m) cipher text, encrypted with key KA m = KB(KA(m)) plaintext plaintextciphertext K A encryption algorithm decryption algorithm Sender Receive r K B
- 5. 8-5 Symmetric key cryptography symmetric key crypto: sender and receiver share same (symmetric) key: K e.g., key is knowing substitution pattern in mono alphabetic substitution cipher plaintextciphertext K S encryption algorithm decryption algorithm S K S plaintext message, m K (m) S m = KS(KS(m))
- 6. 8-6 Simple encryption scheme substitution cipher: substituting one thing for another monoalphabetic cipher: substitute one letter for another plaintext: abcdefghijklmnopqrstuvwxyz ciphertext: mnbvcxzasdfghjklpoiuytrewq Plaintext: bob. i love you. alice ciphertext: nkn. s gktc wky. mgsbc e.g.: Encryption key: mapping from set of 26 letters to set of 26 letters
- 7. 8-7 A more sophisticated encryption approach n substitution ciphers, M1,M2,…,Mn cycling pattern: e.g., n=4: M1,M3,M4,M3,M2; M1,M3,M4,M3,M2; .. for each new plaintext symbol, use subsequent substitution pattern in cyclic pattern dog: d from M1, o from M3, g from M4 Encryption key: n substitution ciphers, and cyclic pattern key need not be just n-bit pattern
- 8. 8-8 Symmetric key crypto: DES DES: Data Encryption Standard 56-bit symmetric key, 64-bit plaintext input block cipher with cipher block chaining making DES more secure: 3DES: encrypt 3 times with 3 different keys
- 9. 8-9 Symmetric key crypto: DES initial permutation 16 identical “rounds” of function application, each using different 48 bits of key final permutation DES operation
- 10. 8-10 AES: Advanced Encryption Standard processes data in 128 bit blocks 128, 192, or 256 bit keys brute force decryption (try each key) taking 1 sec on DES, takes 149 trillion years for AES
- 11. 8-11 Public Key Cryptography symmetric key crypto requires sender, receiver know shared secret key public key crypto radically different approach [Diffie- Hellman76, RSA78] sender, receiver do not share secret key public encryption key known to all private decryption key known only to receiver
- 12. 8-12 Public key cryptography plaintext message, m ciphertextencryption algorithm decryption algorithm receiver’s public key plaintext messageK (m) B + K B + receiver’s private key K B - m = K (K (m))B + B -
- 13. 8-13 Public key encryption algorithms need K ( ) and K ( ) such thatB B . . given public key K , it should be impossible to compute private key K B B requirements: 1 2 RSA: Rivest, Shamir, Adelson algorithm + - K (K (m)) = m BB - + + -
- 14. 8-14 RSA modular arithmetic (a mod n)d mod n = ad mod n assume: a=14, n=10, d=2: (a mod n)d mod n = 42 mod 10 = 6 ad = 142 = 196 ad mod 10 = 6
- 15. 8-15 RSA: Creating public/private key pair 1. choose two large prime numbers p, q. (e.g., 1024 bits each) 2. compute n = pq, z = (p-1)(q-1) 3. choose e (with e<n) that has no common factors with z (e, z are “relatively prime”). 4. choose d such that ed-1 is exactly divisible by z. (in other words: ed mod z = 1 ). 5. public key is (n,e). private key is (n,d). K B + K B -
- 16. 8-16 RSA: encryption, decryption 0. given (n,e) and (n,d) as computed above 1. to encrypt message m (<n), compute c = m mod ne 2. to decrypt received bit pattern, c, compute m = c mod nd m = (m mod n)e mod n dmagic happens! c
- 17. 8-17 RSA example: Let p=5, q=7. Then n=35, z=24. e=5 (so e, z relatively prime). d=29 (so ed-1 exactly divisible by z). bit pattern m m e c = m mod ne 0000l000 12 24832 17 encrypt: encrypting 8-bit messages. c m = c mod nd 17 481968572106750915091411825223071697 12 c d decrypt:
- 18. 8-18 Why does RSA work? must show that cd mod n = m where c = me mod n fact: for any x and y: xy mod n = x(y mod z) mod n where n= pq and z = (p-1)(q-1) thus, cd mod n = (me mod n)d mod n = med mod n = m(ed mod z) mod n = m1 mod n = m
- 19. 8-19 RSA: another important property The following property will be very useful later: K (K (m)) = m BB - + K (K (m))BB + - = use public key first, followed by private key use private key first, followed by public key result is the same!
- 20. 8-20 Why is RSA secure? suppose you know Bob’s public key (n,e). How hard is it to determine d? essentially need to find factors of n without knowing the two factors p and q fact: factoring a big number is hard
- 21. 8-21 RSA in practice: session keys exponentiation in RSA is computationally intensive DES is at least 100 times faster than RSA use public key crypto to establish secure connection, then establish second key – symmetric session key – for encrypting data
- 22. 8-22 large message m H(m) Receiver’s private key KB - + sender sends digitally signed message: Receiver verifies signature, integrity of digitally signed message: KB(H(m)) - encrypted msg digest KB(H(m)) - encrypted msg digest large message m H(m) H(m) recev’s public key KB + equal ? Digital signature = signed message digest
- 23. 8-23 Secure e-mail sender wants to provide secrecy, sender authentication, message integrity. Sender uses three keys: his private key, receiver’s public key, newly created symmetric key H( ). KA( ).- + KA(H(m)) - m KA - m KS( ). KB( ).+ + KB(KS ) + KS KB + Internet KS