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ECE-8843 csc.gatech/copeland/jac/8843/ Prof. John A. Copeland

ECE-8843 http://www.csc.gatech.edu/copeland/jac/8843/ Prof. John A. Copeland john.copeland@ece.gatech.edu 404 894-5177 fax 404 894-0035 Office: GCATT Bldg 579 email or call for office visit, or call Kathy Cheek, 404 894-5696 Chapter 3 - Public-Key Cryptography & Authentication.

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ECE-8843 csc.gatech/copeland/jac/8843/ Prof. John A. Copeland

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  1. ECE-8843 http://www.csc.gatech.edu/copeland/jac/8843/ Prof. John A. Copeland john.copeland@ece.gatech.edu 404 894-5177 fax 404 894-0035 Office: GCATT Bldg 579 email or call for office visit, or call Kathy Cheek, 404 894-5696 Chapter 3 - Public-Key Cryptography & Authentication

  2. Authentication Requirements - must be able to verify that: 1. Message came from apparent source or author, 2. Contents have not been altered, 3. Sometimes, it was sent at a certain time or sequence. Sometimes we would like to provide authentication without encryption (public statements do not need privacy). Still, authentication requires that the sender know something that the forger does not ( a secret key). Conventional encryption can be used, but the sender must share the secret key with the receiver. 2

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  4. (b) Using public-key encryption 4

  5. Secret Value is added by both parties to message before the “hash,” function is used to get the Message Integrity Check (MIC). It is removed before transmission. MIC MIC It is critical that a forger can not compose a different message that would produce the same MIC value. 5

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  7. SHA-1 Secure Hash Algorithm 1 7

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  9. HMAC Structure 9

  10. Public-Key Cryptography (Public-Private Key) plaintext (data file or message) encryption by key-1 decryption by key-1 ciphertext (stored or transmitted safely) decryption by key-2 encryption by key-2 plaintext (original data or message) 10

  11. Encryption using a Public-Key System 11

  12. Authentication using a Public-Key System 12

  13. RSA (Rivest, Shamir, and Adleman) Key length is variable, 512 bits most common. • The plaintext block ("m") must be less than the key length. Key Generation • Choose two large prime numbers, p and q (secret) • n = pq, Ø(n) = (p-1)(q-1) • Find a number, e, that is relatively prime to Ø(n) • The public key is e and n (e,n) • Find d, the multiplicative inverse to e mod Ø(n) (by “Number Theory”: d * e mod Ø(n) = 1) The private key is d and n (d,n), public key is (e,n) Encryption: c = m^e mod n ("m" is message) Decryption: m = c^d mod n ("c" is ciphertext) 13

  14. Is RSA Secure? To factor a 512-bit number (to find p and q from n) with the best known technique would take 500,000 MIPs-years • In 500 years on a 1000 MIP/s CPU, an eavesdropper can encrypt a list of all possible messages (using the Public Key), and compare the corresponding ciphertext to the transmitted ciphertext. • If the message is your password, make sure you picked a good one (not in any dictionary). • A defense is to add random bits to the message. MIPs - Millions of Instructions per second. 14

  15. How Efficient are RSA Operations Efficient techniques for doing exponentiation: X * Y mod n = (X mod n) * (Y mod n) • Do a "mod n" operation whenever a multiplier is bigger than n To calculate x^10 1 1011101100001 mod n 2 x^10 = (x^1 )^2 2 2 x^100 = (x^10 )^2 2 2 x^(10 1 ) = (x^100 ) * x 15 2 2

  16. Does It Work? (Does D(E(m))=m) c = E(m) =(m ^ e) mod n (the ciphertext) D(c) = (c ^ d) mod n (decryption of c) = m^(e*d) mod n = m^(e*d mod Ø(n)) mod n (Number Theory) = m^(1) mod n = m (the plaintext message) To experiment use: www.csc.gatech.edu/copeland/jac/8843/tools/RSA.xls 16

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  18. Public-Key Systems Encrypt/ Digital Key Decrypt Signature Exchange RSA X X X Diffie-Hellman X X DSS X Elliptic Curve X X X 18

  19. Diffie-Hellman Technique Mutual Secret Keys or Public-Private Keys Global Public Elements: q (large prime) and a (a < q) User A‘s Keys: Select secret Xa (Xa < q) Public Key is Ya = a^Xa mod q User B‘s Keys: Select secret Xb (Xb < q) Public Key is Yb = a^Xb mod q Mutual Key is K = Yb ^Xa (A’s calculation) Ya ^ Xb (B’s calculation) a^(Xa*Xb) mod q (in both cases) No one else knows either Xa or Xb, so they can not find out K 19

  20. Diffie-Hellman as used for a Public-Private System + a and q + message encrypted with “ K” B has to send “ Yb” with message so A can decrypt it. (Ya, a,q are A’s Public Key) “Trudie” does not know Xa: Can not read message. 20

  21. Raw “Certificate” has user name, public key, expiration date, ... Generate hash code of Raw Certificate Raw Cert. MIC Hash Encrypt hash code with CA’s private key to form CA’s signature Signed Cert. Signed Certificate Recipient can verify signature using CA’s public key. Certificate Authority generates the “signature” that is added to raw “Certificate” 21

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