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Key Management
- 1. Key Management PRESENTED BY– MD. SADIQUL AMIN STUDENT ID – 1510876117 COMPUTER SCIENCE & ENGINEERING DEPARTMENT UNIVERSITY OF RAJSHAHI 1
- 2. Key Distribution Several techniqueshave been proposed for the distribution of public keys. 1. Public Announcement. 2. Publicly Available Directory. 3. Public-key Authority. 4. Public-key Certificates. 2
- 3. Public Announcement Okay, Iwill send message using 234adfg4dg4 3
- 4. Public Announcement -Limitation Okay, I will send message using CCCCCCC Alif Bob Chris 4
- 5. Publicly Available Directory Iam ALIF. My PUBLIC KEY (Ku) is 234adfg4dg4 Directory {ALIF - 234adfg4dg4 } {BOB - kdsfdghd5d7 } I am BOB. My PUBLIC KEY (Ku) is kdsfghd5d4 5
- 6. Public-Key Authority Authority {ALIF - 234adfg4dg4} {BOB - kdsfdghd5d7 } I am ALIF. This 8 pm, I need BOBs public key. ENCRYPTED 𝐾𝑈𝐴𝑢𝑡ℎ 6
- 7. Public-Key Authority Authority {ALIF - 234adfg4dg4} {BOB - kdsfdghd5d7 } 1. BOBs KU is kdsfdghd5d 2. Your request was “I am ALIF. This 8 pm, I need BOBs public key.” 3. You asked for it at 8 p.m. ENCRYPTED 𝐾𝑅 𝐴𝑢𝑡ℎ 7
- 8. Public-Key Authority Hi, Iam ALIF. My number is 546455 and the message ID is 555. ENCRYPTED 𝐾𝑈 𝐵𝑂𝐵 8
- 9. Public-Key Authority Authority {ALIF - 234adfg4dg4} {BOB - kdsfdghd5d7 } I am BOB. This 9 pm, I need ALIFs public key. LOCKED 𝐾𝑈𝐴𝑢𝑡ℎ 9
- 10. Public-Key Authority Authority {ALIF - 234adfg4dg4} {BOB - kdsfdghd5d7 } 1. ALIFs KU is 234adfg4dg4 2. Your request was “I am BOB. This 9 pm, I need ALIFs public key.” 3. You asked for it at 9 p.m. ENCRYPTED 𝐾𝑅 𝐴𝑢𝑡ℎ 10
- 11. Public-Key Authority Hi, Iam BOB. My number is 123645 and the message ID is 678. Your message ID was 555. LOCKED 𝐾𝑈𝐴𝐿𝐼𝐹 11
- 12. Public-Key Authority Your messageID was 678 LOCKED 𝐾𝑈 𝐵𝑂𝐵 12
- 13. Public-Key Certificates Authority I amALIF. My PUBLIC KEY (𝐾𝑈𝐴𝐿𝐼𝐹) is 234adfg4dg4 13
- 14. Public-Key Certificates Authority Time –201902051120 ID – 0001 PUBLIC KEY - 234adfg4dg4 ENCRYPTED 𝐾𝑅 𝐴𝑢𝑡ℎ 14
- 15. Public-Key Certificates Authority I amBOB. My PUBLIC KEY (𝐾𝑈 𝐵𝑂𝐵) is kdsfdghd5d7 15
- 16. Public-Key Certificates Authority Time –201902051120 ID – 0009 PUBLIC KEY - kdsfdghd5d7 ENCRYPTED 𝐾𝑅 𝐴𝑢𝑡ℎ 16
- 17. Public-Key Certificates Time –201902051120 ID – 0001 PUBLIC KEY - 234adfg4dg4 ENCRYPTED 𝐾𝑅 𝐴𝑢𝑡ℎ 17
- 18. Public-Key Certificates Time –201902051120 ID – 0001 PUBLIC KEY - 234adfg4dg4 ENCRYPTED 𝐾𝑅 𝐴𝑢𝑡ℎ 18
- 19. Diffie-Hellman Key Exchange Primitive Roots 27 mod 13 = 11 28 mod 13 = 9 29 mod 13 = 5 210 mod 13 = 10 211 mod 13 = 7 212 mod 13 = 1 21 mod 13 = 2 22 mod 13 = 4 23 mod 13 = 8 24 mod 13 = 3 25 mod 13 = 6 26 mod 13 = 12 19
- 20. Diffie-Hellman Key Exchange Discrete Logarithm For any integer b and a primitive root a of prime number p, we can find a unique exponent i such that b ≡ ai mod p where 0 ≤ i ≤ (p-1) The exponent i is referred to as the discrete logarithm of b for the base a, mod p. We express this value as 𝑑𝑙𝑜𝑔 𝑎,𝑝(𝑏) 20
- 21. Diffie-Hellman Key Exchange Public Numbers – a prime number q , an intiger a such that a primitive root of q, 𝒀 𝑨, 𝒀 𝑩(calculated). Private Numbers – randomly selected 𝑿 𝑨, 𝑿 𝑩where X < q 21
- 22. Diffie-Hellman Key Exchange UserA selects a random integer XA<q and computes YA = αXA mod q. Similarly B selects a random integer XB<q and computes YB = αXB mod q. Each side keeps X value as private and Y value as public. User A computes the key as K = (YB)XA mod q and B computes the key as K=(YA)XB mod q. 22
- 23. Diffie-Hellman Key Exchange Thesetwo calculations produce identical results: K=(YB)XA mod q =(αXB mod q)XA mod q =(αXB)XA mod q by modular rules. =αXBXA mod q =(αXA)XB mod q =(αXA mod q)XB mod q =(YA)XB mod q 23
- 24. Diffie-Hellman Key Exchange Theattacker may compute XB = indα,q(YB) to get secret key of B. The security of Diffie-Hellman key exchange lies in the fact that, while it is relatively easy to calculate exponentials modulo a prime, it is very difficult to calculate discrete logarithms. For large prime the later task is infeasible. 24
- 25. Any Questions? 25
- 26.