How to Send a Secret Message

https://github.com/breandan/crypto-exercises

Transcript

1. How to Send a Secret Message GZS WZ PMJR Y PMTDMW NMPPYKM Breandan Considine QDMYJRYJ TZJPOROJM Nikhil Nanivadekar JOBGOC JYJOVYRMBYD
2. What is cryptology?
3. Cryptology is the study of codes.
4. U V W X Y Z A B C D E F G H I J K L M N O Q P R S T 1 2 3 4 5 6 7 8 9 0
8. Cryptology is the study of codes. ^ secret
9. Cryptology is the study of codes. ^ secret TOP SECRET
10. How do you share a secret message?
11. Let’s meet Tuesday afternoon at three.
12. Let’s meet Tuesday afternoon at three.
13. Let’s meet Tuesday afternoon at three. Lxt’s mxxt Tuxsday aftxrnoon at thrxx.
14. Can we do better?
15. Exercise #1: Let’s write a cipher!
16. What is a key?
19. One path forward... Many paths backward
20. Exercise #2: Let’s crack a cipher!
21. Just like the key, a message can be...
22. 907461028 123877499 129830976 123974729
23. “three o’clock”
24. “ ” हहलल वररर
26. Exercise #3: What is a key?
27. What happens if someone learns our algorithm?
28. What happens if someone learns our message?
29. What happens if someone learns our key?
30. What is a prime number?
35. 31 32 33 34 35 36 37 13 14 15 16 17 30 38 3 4 5 12 18 29 39 1 2 6 11 19 28 40 7 8 9 10 20 27 41 21 22 23 24 25 26 42 43 44 45 46 47 48 49...
36. 31 37 13 17 3 5 29 2 11 19 7 41 23 43 47 ...
38. How do we know if an integer is a prime number?
39. Exercise #4: What is an algorithm?
40. Can we share a secret message without sharing a secret key?
41. One day in 1977...
42. Exercise #5: What is a public key?
43. Step #1: Choose two large random prime numbers (p, q)
44. Step #2: Choose a number e, that is co-prime to (p-1)(q-1) (let’s call ^ φ)
45. Step #3: Publish p*q and e.
46. Step #5: Encrypt with c(m) = me (mod pq)
47. Step #6: Decrypt with p(c) = cd (mod pq)
48. Step #6a: Where d is the inverse modulus of e (mod φ) ie. e*d = 1 (mod (p-1)(q-1))
49. Step #2: Choose a number e, that is co-prime to (p-1)(q-1)
50. Step #2: Choose a number e, that is co-prime to (p-1)(q-1)
51. Exercise #6: Solve for d.