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Lecture 24 Cryptography

Lecture 24 Cryptography. CPE 401 / 601 Computer Network Systems. slides are modified from Jim Kurose and Keith Ross and Dave Hollinger. Cryptography. Encryption Scramble data so that only someone with a secret can make sense of the data. Decryption Descrambling encrypted data. K. K.

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Lecture 24 Cryptography

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  1. Lecture 24Cryptography CPE 401 / 601Computer Network Systems slides are modified from Jim Kurose and Keith Ross and Dave Hollinger

  2. Cryptography • Encryption • Scramble data so that only someone with a secret can make sense of the data. • Decryption • Descrambling encrypted data. Cryptography

  3. K K A B The language of cryptography Alice’s encryption key Bob’s decryption key symmetric key crypto: sender, receiver keys identical public-key crypto: encryption key public, decryption key secret (private) encryption algorithm decryption algorithm ciphertext plaintext plaintext Cryptography

  4. Symmetric key cryptography substitution cipher: substituting one thing for another • monoalphabetic cipher: substitute one letter for another plaintext: abcdefghijklmnopqrstuvwxyz ciphertext: mnbvcxzasdfghjklpoiuytrewq E.g.: Plaintext: bob. i love you. alice ciphertext: nkn. s gktc wky. mgsbc • Q: How hard to break this simple cipher? • brute force? • other? Cryptography

  5. K K A-B A-B K (m) m = K ( ) A-B A-B Symmetric key cryptography symmetric key crypto: Bob and Alice share know same (symmetric) key: K • e.g., key is knowing substitution pattern in mono alphabetic substitution cipher • Q: how do Bob and Alice agree on key value? encryption algorithm decryption algorithm ciphertext plaintext plaintext message, m K (m) A-B A-B Cryptography

  6. DES: Data Encryption Standard • US encryption standard [NIST 1993] • 56-bit symmetric key, 64-bit plaintext input • How secure is DES? • DES Challenge: 56-bit-key-encrypted phrase “Strong cryptography makes the world a safer place” decrypted (brute force) in 4 months • no known “backdoor” decryption approach • making DES more secure: • use three keys sequentially (3-DES) on each datum • use cipher-block chaining Cryptography

  7. DES operation DES initial permutation 16 identical “rounds” of function application, each using different 48 bits of key final permutation Cryptography

  8. AES: Advanced Encryption Standard • symmetric-key NIST standard • replacing DES • Nov 2001 • 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 Cryptography

  9. T1 T8 T7 T5 T6 T4 T3 T2 Block Cipher 64-bit input 8bits 8bits 8bits 8bits 8bits 8bits 8bits 8bits loop for n rounds 8 bits 8 bits 8 bits 8 bits 8 bits 8 bits 8 bits 8 bits 64-bit scrambler 64-bit output • one pass through: input bit affects eight output bits • multiple passes: each input bit afects all output bits • block ciphers: DES, 3DES, AES Cryptography

  10. Public key cryptography symmetric key crypto • requires sender, receiver know shared secret key • Q: how to agree on key in first place • particularly if never “met”? public key cryptography • 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 Cryptography

  11. + K (m) B - + m = K (K (m)) B B Public key cryptography + Bob’s public key K B - Bob’s private key K B encryption algorithm decryption algorithm plaintext message plaintext message, m ciphertext Cryptography

  12. K (K (m)) = m B B - + 2 1 Public key encryption algorithms Requirements: need K ( ) and K ( ) such that . . + - B B + given public key K , it should be impossible to compute private key K B - B RSA: Rivest, Shamir, Adleman algorithm Cryptography

  13. + - K K B B RSA: Choosing keys 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). Cryptography

  14. 1. To encrypt bit pattern, m, compute d e c = m mod n m = c mod n e (i.e., remainder when m is divided by n) d e m = (m mod n) mod n RSA: Encryption, decryption 0. Given (n,e) and (n,d) as computed above 2. To decrypt received bit pattern, c, compute d (i.e., remainder when c is divided by n) Magic happens! c Cryptography

  15. d e c = m mod n m = c mod n d c RSA example: Bob chooses 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. e m m letter encrypt: l 17 1524832 12 c letter decrypt: 17 12 l 481968572106750915091411825223071697 Cryptography

  16. e d ed (m mod n) mod n = m mod n ed mod (p-1)(q-1) 1 = m mod n = m = m mod n y y mod (p-1)(q-1) d e x mod n = x mod n m = (m mod n) mod n RSA: Why is that Useful number theory result: If p,q prime and n = pq, then: (using number theory result above) (since we choseed to be divisible by (p-1)(q-1) with remainder 1 ) Cryptography

  17. K (K (m)) = m - B B + K (K (m)) - + = B B RSA: another important property The following property will be very useful later: use private key first, followed by public key use public key first, followed by private key Result is the same! Cryptography

  18. Using Keys • Private keys are used for decrypting • Public keys are used for encrypting encryption plaintext ciphertext public key decryption ciphertext plaintext private key Cryptography

  19. Transmitting over an insecure channel Alice wants to send Bob a private message. Apublicis Alice’s public key. Aprivateis Alice’s private key. Bpublicis Bob’s public key. Bprivateis Bob’s private key. Cryptography

  20. Hello Bob,Wanna get together? Alice Bob encrypt using Bpublic decrypt using Bprivate Cryptography

  21. OK Alice,Your place or mine? Alice Bob decrypt using Aprivate encrypt using Apublic Cryptography

  22. Bob’s Dilemma • Nobody can read the message from Alice, but anyone could produce it. • How does Bob know that the message was really sent from Alice? • Bob may be comforted to know that only Alice can read his reply. Cryptography

  23. Alice can sign her message! • Alice can create a digital signature and prove she sent the message • or someone with knowledge of her private key • The signature can be a message digest encrypted with Aprivate. Cryptography

  24. Message Digest • Also known as “hash function” or “one-way transformation”. • Transforms a message of any length and computes a fixed length string. • We want it to be hard to guess what the message was given only the digest. • Guessing is always possible. Cryptography

  25. Digital Signature • Public key cryptography is also used to provide digital signatures signing plaintext signed message private key verification signed message plaintext public key Cryptography

  26. Alice’s Signature • Alice feeds her original message through a hash function and encrypts the message digest with Aprivate. • Bob can decrypt the message digest using Apublic. • Bob can compute the message digest himself. • If the 2 message digests are identical, Bob knows Alice sent the message. Cryptography

  27. Revised Scheme Alice Bob Sign with Aprivate check signature using Apublic decrypt using Bprivate encrypt using Bpublic Cryptography

  28. Why the digest? • Alice could just encrypt her name, and then Bob could decrypt it with Apublic. • Why wouldn’t this be sufficient? • Suppose Alice denies she sent the message? • Bob can prove that only someone with Alice’s key could have produced the message. Cryptography

  29. Solution? • Always start your messages with: • Dear Mehmet, • Create a digest from the encrypted message and sign that digest. • There are many other schemes as well. Cryptography

  30. Speed • Secret key encryption/decryption algorithms are much faster than public key algorithms. • Many times a combination is used: • use public key cryptography to share a secret key. • use the secret key to encrypt the bulk of the communication. Cryptography

  31. Authentication Goal:Bob wants Alice to “prove” her identity to him Protocol 1.0:Alice says “I am Alice” “I am Alice” Failure scenario?? Cryptography

  32. Authentication Goal: Bob wants Alice to “prove” her identity to him Protocol 1.0:Alice says “I am Alice” in a network, Bob cannot “see” Alice, so Trudy simply declares herself to be Alice “I am Alice” Cryptography

  33. Alice’s IP address “I am Alice” Authentication: another try Protocol 2.0:Alice says “I am Alice”in an IP packet containing her source IP address Failure scenario?? Cryptography

  34. Alice’s IP address “I am Alice” Authentication: another try Protocol 2.0:Alice says “I am Alice”in an IP packet containing her source IP address Trudy can create a packet “spoofing” Alice’s address Cryptography

  35. Alice’s password Alice’s IP addr “I’m Alice” Alice’s IP addr OK Authentication: another try Protocol 3.0:Alice says “I am Alice” and sends her secret password to “prove” it. Failure scenario?? Cryptography

  36. Alice’s password Alice’s IP addr “I’m Alice” Alice’s IP addr OK Authentication: another try Protocol 3.0:Alice says “I am Alice” and sends her secret password to “prove” it. Alice’s password Alice’s IP addr “I’m Alice” playback attack:Trudy records Alice’s packet and later plays it back to Bob Cryptography

  37. encrypted password Alice’s IP addr “I’m Alice” Alice’s IP addr OK Authentication: yet another try Protocol 3.1:Alice says “I am Alice” and sends her encrypted secret password to “prove” it. Failure scenario?? Cryptography

  38. encrypted password Alice’s IP addr “I’m Alice” Alice’s IP addr OK Authentication: yet another try Protocol 3.1:Alice says “I am Alice” and sends her encrypted secret password to “prove” it. encrypted password Alice’s IP addr “I’m Alice” Record and playback still works! Cryptography

  39. K (R) A-B Authentication: yet another try Goal:avoid playback attack Nonce:number (R) used only once–in-a-lifetime 4.0:to prove Alice “live”, Bob sends Alice nonce, R. Alice must return R, encrypted with shared secret key “I am Alice” R Alice is live, and only Alice knows key to encrypt nonce, so it must be Alice! Cryptography

  40. - K (R) A + + K K A A - - + (K (R)) = R K (K (R)) = R A A A Authentication: ap5.0 ap4.0 requires shared symmetric key • can we authenticate using public key techniques? ap5.0: use nonce, public key cryptography “I am Alice” Bob computes R and knows only Alice could have the private key, that encrypted R such that “send me your public key” Cryptography

  41. Man (woman) in the middle attack: Trudy poses as Alice (to Bob) and as Bob (to Alice) - - K (R) K (R) A T + + K K A T - - + + m = K (K (m)) m = K (K (m)) + + A T A T K (m) K (m) A T ap5.0: security hole I am Alice I am Alice R R Send me your public key Send me your public key Trudy gets sends m to Alice encrypted with Alice’s public key Cryptography

  42. Man (woman) in the middle attack: Trudy poses as Alice (to Bob) and as Bob (to Alice) ap5.0: security hole • Difficult to detect: • Bob receives everything that Alice sends, and vice versa. (e.g., so Bob, Alice can meet one week later and recall conversation) • problem is that Trudy receives all messages as well! Cryptography

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