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Cryptography Lecture 0 Manoj Prabhakaran University of Illinois Urbana-Champaign In the News Properly implemented strong crypto systems are one of the few things that you can rely on. In the News Properly implemented strong

  1. Cryptography Lecture 0 Manoj Prabhakaran University of Illinois Urbana-Champaign

  2. In the News “Properly implemented strong crypto systems are one of the few things that you can rely on. ”

  3. In the News “Properly implemented strong crypto systems are one of the few things that you can rely on. ” “… Unfortunately, endpoint security is so terrifically weak that [the adversary] can frequently find ways around it. ”

  4. What is Cryptography?

  5. What is Cryptography? It’ s all about controlling access to information

  6. What is Cryptography? It’ s all about controlling access to information A tool for enforcing policies on who can learn and/or influence information

  7. What is Cryptography? It’ s all about controlling access to information A tool for enforcing policies on who can learn and/or influence information Do we know what we are talking about?

  8. What is information?

  9. What is information? Or rather the lack of it?

  10. What is information? Or rather the lack of it? Uncertainty

  11. What is information? Or rather the lack of it? Uncertainty The word is Entropy

  12. What is information? Or rather the lack of it? Uncertainty The word is Entropy Borrowed from thermodynamics

  13. What is information? Rudolf Clausius Or rather the lack of it? Uncertainty The word is Entropy Borrowed from thermodynamics

  14. What is information? Rudolf Clausius Ludwig Boltzmann Or rather the lack of it? Uncertainty The word is Entropy Borrowed from thermodynamics

  15. What is information? Rudolf Clausius Ludwig Boltzmann Or rather the lack of it? Claude Shannon Uncertainty The word is Entropy Borrowed from thermodynamics

  16. What is information? Rudolf Clausius Ludwig Boltzmann Or rather the lack of it? Claude Shannon Uncertainty The word is Entropy Borrowed from thermodynamics An inherently “probabilistic” notion

  17. What is information? Claude Shannon

  18. What is information? Information Theory: ways to quantify information Claude Shannon

  19. What is information? Information Theory: ways to quantify information Application 1: to study efficiency of communication (compression, Claude Shannon error-correction)

  20. What is information? Information Theory: ways to quantify information Application 1: to study efficiency of communication (compression, Claude Shannon error-correction) Application 2: to study the possibility of secret communication

  21. What is information? Information Theory: ways to quantify information Application 1: to study efficiency of communication (compression, Claude Shannon error-correction) Application 2: to study the possibility of secret communication The latter turned out to be a relatively easy question! Secret communication possible only if (an equally long) secret key is shared ahead of time

  22. Access to Information

  23. Access to Information A second look

  24. Access to Information A second look Information at hand may still not be “accessible” if it is hard to work with it

  25. Access to Information A second look Information at hand may still not be “accessible” if it is hard to work with it Computation!

  26. Access to Information A second look Information at hand may still not be “accessible” if it is hard to work with it Computation! Shannon’ s information may reduce uncertainty only for computationally all-powerful parties

  27. Computational Complexity

  28. Computational Complexity A systematic study of what computationally bounded parties can and cannot do

  29. Computational Complexity Alan Turing A systematic study of what Stephen Cook computationally bounded parties can and cannot do A young and rich field Leonid Levin Richard Karp

  30. Computational Complexity Alan Turing A systematic study of what Stephen Cook computationally bounded parties can and cannot do A young and rich field Much known, much more unknown Leonid Levin Richard Karp

  31. Computational Complexity Alan Turing A systematic study of what Stephen Cook computationally bounded parties can and cannot do A young and rich field Much known, much more unknown Much “believed” Leonid Levin Richard Karp

  32. Computational Complexity Alan Turing A systematic study of what Stephen Cook computationally bounded parties can and cannot do A young and rich field Much known, much more unknown Much “believed” Leonid Levin Richard Karp Basis of the Modern Theory of Cryptography

  33. Compressed Secret-Keys

  34. Compressed Secret-Keys Impossible in the information-theoretic sense: 
 a truly random string cannot be compressed

  35. Compressed Secret-Keys Impossible in the information-theoretic sense: 
 a truly random string cannot be compressed But possible against computationally bounded players: use pseudo-random strings!

  36. Compressed Secret-Keys Impossible in the information-theoretic sense: 
 a truly random string cannot be compressed But possible against computationally bounded players: use pseudo-random strings! Pseudo-random number generator

  37. Compressed Secret-Keys Impossible in the information-theoretic sense: 
 a truly random string cannot be compressed But possible against computationally bounded players: use pseudo-random strings! Pseudo-random number generator a.k.a Stream Cipher

  38. Compressed Secret-Keys Impossible in the information-theoretic sense: 
 a truly random string cannot be compressed But possible against computationally bounded players: use pseudo-random strings! Pseudo-random number generator a.k.a Stream Cipher Manuel Blum Andy Yao Generate a long string of random-looking bits from a short random seed

  39. The Public-Key Revolution

  40. The Public-Key Revolution “Non-Secret Encryption” James Ellis

  41. The Public-Key Revolution “Non-Secret Encryption” No a priori shared secrets James Ellis

  42. The Public-Key Revolution “Non-Secret Encryption” No a priori shared secrets James Ellis Instead, a public key. Anyone can create encryptions, only the creator of the key can decrypt!

  43. The Public-Key Revolution “Non-Secret Encryption” No a priori shared secrets Clifford Cocks James Ellis Instead, a public key. Anyone can create encryptions, only the creator of the key can decrypt!

  44. The Public-Key Revolution “Non-Secret Encryption” Malcolm Williamson No a priori shared secrets Clifford Cocks James Ellis Instead, a public key. Anyone can create encryptions, only the creator of the key can decrypt!

  45. The Public-Key Revolution “Non-Secret Encryption” Malcolm Williamson No a priori shared secrets Clifford Cocks James Ellis Instead, a public key. Anyone can create encryptions, only the creator of the key can decrypt! Merkle, Hellman, Diffie

  46. The Public-Key Revolution “Non-Secret Encryption” Malcolm Williamson No a priori shared secrets Clifford Cocks James Ellis Instead, a public key. Anyone can create encryptions, only the creator of the key can decrypt! Publicly verifiable digital signatures Merkle, Hellman, Diffie Shamir, Rivest, Adleman

  47. The Public-Key Revolution “Non-Secret Encryption” Malcolm Williamson No a priori shared secrets Clifford Cocks James Ellis Instead, a public key. Anyone can create encryptions, only the creator of the key can decrypt! Publicly verifiable digital signatures Merkle, Hellman, Diffie Forms the backbone of today’ s secure communication Shamir, Rivest, Adleman

  48. Crypto-Mania

  49. Crypto-Mania Public-Key cryptography and beyond!

  50. Crypto-Mania Public-Key cryptography and beyond! Secret computation: collaboration among mutually distrusting parties

  51. Crypto-Mania Public-Key cryptography and beyond! Secret computation: collaboration among mutually distrusting parties Compute on distributed data, without revealing their private information to each other

  52. Crypto-Mania Public-Key cryptography and beyond! Secret computation: collaboration among mutually distrusting parties Compute on distributed data, without revealing their private information to each other Compute on encrypted data

  53. Crypto-Mania Public-Key cryptography and beyond! Secret computation: collaboration among mutually distrusting parties Compute on distributed data, without revealing their private information to each other Compute on encrypted data And other fancy things... with sophisticated control over more complex “access” to information

  54. Crypto-Mania Public-Key cryptography and beyond! Secret computation: collaboration among mutually distrusting parties Compute on distributed data, without revealing their private information to each other Compute on encrypted data And other fancy things... with sophisticated control over more complex “access” to information Do it all faster, better, more conveniently and more securely (or find out if one cannot). And also make sure we know what we are trying to do.

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