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CS/COE 1501 Recitation Extended Euclidean Algorithm + Digital Signatures.

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Presentation on theme: "CS/COE 1501 Recitation Extended Euclidean Algorithm + Digital Signatures."— Presentation transcript:

1 CS/COE 1501 Recitation Extended Euclidean Algorithm + Digital Signatures

2 Extended Euclidean Algorithm

3 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978 2 3 4 5 6

4 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781 2 3 4 5 6

5 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 2 3 4 5 6

6 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 2 3 4 5 6

7 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821 3 4 5 6

8 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 278213 3 4 5 6

9 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3 4 5 6

10 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 32115 4 5 6

11 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 321151 4 5 6

12 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 5 6

13 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 6 5 6

14 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 62 5 6

15 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 5 6

16 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 563 6

17 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 5632 6

18 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 56320 6

19 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 56320 630

20 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 56320 630NaN

21 Extended Euclidean Algorithm

22 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 56320 630NaN

23 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 56320 630NaN 310

24 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 19978121 27821315 3211516 4 623 56320 630NaN 310

25 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 6233 563203 630NaN 310

26 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 6233 563203 630NaN 310

27 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 6233 5632030 630NaN 310

28 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 6233 5632030 630NaN 310

29 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 6233 56320301 630NaN 310

30 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 6233 56320301 630NaN 310

31 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 6233 56320301 630NaN 310

32 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 62331 56320301 630NaN 310

33 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 62331-2 56320301 630NaN 310

34 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 62331-2 56320301 630NaN 310

35 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163 4 62331-2 56320301 630NaN 310

36 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163-2 41562331-2 56320301 630NaN 310

37 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163-23 41562331-2 56320301 630NaN 310

38 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163-23 41562331-2 56320301 630NaN 310

39 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 278213153 32115163-23 41562331-2 56320301 630NaN 310

40 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 2782131533 32115163-23 41562331-2 56320301 630NaN 310

41 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213 2782131533-11 32115163-23 41562331-2 56320301 630NaN 310

42 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213-11 2782131533-11 32115163-23 41562331-2 56320301 630NaN 310

43 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213-1114 2782131533-11 32115163-23 41562331-2 56320301 630NaN 310

44 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213-1114 2782131533-11 32115163-23 41562331-2 56320301 630NaN 310

45 Find the Bézout numbers and GCD of 99 and 78 Rowaba/ba%bdst 199781213-1114 2782131533-11 32115163-23 41562331-2 56320301 630NaN 310

46 Hash Functions

47 For Crypto Hash Functions, Output Should Appear Random

48 Digital Signatures – Public Key Cryptography

49 Creating a Digital Signature

50 Digital Signatures Often Use Commutative Operations

51

52 Plaintext sent by sender

53 Digital Signatures Often Use Commutative Operations Plaintext sent by sender Cryptotext sent by sender using sender’s private key

54 Digital Signatures Often Use Commutative Operations Plaintext sent by sender Cryptotext sent by sender using sender’s private key Sender’s public key

55 Digital Signatures Often Use Commutative Operations Plaintext sent by sender Cryptotext sent by sender using sender’s private key Sender’s public key =

56 Digital Signatures Often Use Commutative Operations Plaintext sent by sender Cryptotext sent by sender using sender’s private key Sender’s public key = Plaintext recovered matches

57 Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes

58 Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM

59 Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM

60 Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM Compute

61 Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM Compute =

62 Because Public-Key crypto can be computationally expensive, often the crypto operations are performed on the securely hashed version of the message rather than the original: Digital Signatures and Hashes Received: HASH ALGORITHM Compute = Match. Signature Verified.

63 Adam J. Lee’s slides from CS 1653 http://www.csee.umbc.edu/~chang/cs203.s09/exteuclid.shtml Acknowledgements

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