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  • Cryptography is the science of writing in secret code and is an ancient art; the first documented use of cryptography in writing dates back to circa 1900 B.C. when an Egyptian scribe used non-standard hieroglyphs in an inscription. Some experts argue that cryptography appeared spontaneously sometime after writing was invented, with applications ranging from diplomatic missives to war-time battle plans.
  • There are two kinds of cryptosystems: symmetric and asymmetric . Symmetric cryptosystems use the same key (the secret key) to encrypt and decrypt a message, and asymmetric cryptosystems use one key (the public key) to encrypt a message and a different key (the private key) to decrypt it. Asymmetric cryptosystems are also called public key cryptosystems.
  • In traditional cryptography, the sender and receiver of a message know and use the same secret key; the sender uses the secret key to encrypt the message, and the receiver uses the same secret key to decrypt the message. This method is known as secret key or symmetric cryptography
  • The main challenge is getting the sender and receiver to agree on the secret key without anyone else finding out. If they are in separate physical locations, they must trust a courier, a phone system, or some other transmission medium to prevent the disclosure of the secret key. Anyone who overhears or intercepts the key in transit can later read, modify, and forge all messages encrypted or authenticated using that key.
  • The generation, transmission and storage of keys is called key management ; all cryptosystems must deal with key management issues. Because all keys in a secret-key cryptosystem must remain secret, secret-key cryptography often has difficulty providing secure key management, especially in open systems with a large number of users.
  • In order to solve the key management problem, Whitfield Diffie and Martin Hellman introduced the concept of public-key cryptography in 1976. Public-key cryptosystems have two primary uses, encryption and digital signatures. In their system, each person gets a pair of keys, one called the public key and the other called the private key. The public key is published, while the private key is kept secret. The need for the sender and receiver to share secret information is eliminated; all communications involve only public keys, and no private key is ever transmitted or shared. In this system, it is no longer necessary to trust the security of some means of communications. The only requirement is that public keys be associated with their users in a trusted (authenticated) manner (for instance, in a trusted directory). Anyone can send a confidential message by just using public information, but the message can only be decrypted with a private key, which is in the sole possession of the intended recipient.
  • Itt project

    3. 3. Cryptography
    4. 4. What is Cryptography? <ul><li>“ hidden writing” </li></ul><ul><li>Until recently: military tool </li></ul><ul><li>Like any military technology: methods change over time </li></ul><ul><li>Two sides: designing codes breaking codes (cryptanalysis) </li></ul><ul><li>Computers have changed both </li></ul>
    5. 5. Brief History of Cryptography <ul><ul><li>What is Cryptography? </li></ul></ul><ul><ul><ul><li>Science of writing secret code </li></ul></ul></ul><ul><ul><li>The first use of cryptography in 1900 B.C. </li></ul></ul><ul><ul><ul><li>Used by Egyptian scribe </li></ul></ul></ul><ul><ul><ul><li>Some experts say it appeared right after writing was invented </li></ul></ul></ul>
    6. 6. Crypto Terms <ul><li>Cryptography – art/science relating to encrypting, decrypting information </li></ul><ul><li>Cryptanalysis – art/science relating to converting cipher text to plaintext without the (secret) key </li></ul><ul><li>Link encryption – the individual application of encryption to data on each link of network </li></ul><ul><li>End to end encryption – the encryption of data from source system to end system </li></ul>
    7. 7. Cryptography Broken Down <ul><ul><li>Two kinds of cryptosystems: </li></ul></ul><ul><ul><ul><li>Symmetric </li></ul></ul></ul><ul><ul><li>Uses the same key (the secret key) to encrypt and decrypt a message. </li></ul></ul><ul><ul><ul><li>Asymmetric </li></ul></ul></ul><ul><ul><ul><li>Uses one key (the public key) to encrypt a message and a different key (the private key) to decrypt the message. </li></ul></ul></ul>
    8. 8. Symmetric Cryptosystem <ul><ul><li>The message: </li></ul></ul><ul><ul><li>The sender and receiver know and use the same secret key. </li></ul></ul><ul><ul><li>The sender uses the secret key to encrypt the message. </li></ul></ul><ul><ul><li>The receiver uses the same secret key to decrypt the message. </li></ul></ul>
    9. 9. Symmetric Cryptosystem
    10. 10. Symmetric Challenge <ul><ul><li>Main challenge: </li></ul></ul><ul><ul><ul><li>Agreeing on the key while maintaining secrecy. </li></ul></ul></ul><ul><ul><ul><li>Trusting a phone system or some transmission medium. </li></ul></ul></ul><ul><ul><ul><li>The interceptor can read, modify, and forge all messages </li></ul></ul></ul>
    11. 11. Key Management <ul><li>The generation, transmission, and storage of a key. </li></ul><ul><li>All cryptosystems must deal with key management issues </li></ul><ul><li>Because all keys must remain secret there is often difficulty providing secure key management. </li></ul>
    12. 12. Introduction of the Public Key <ul><li>Created to solve key management problems. </li></ul><ul><li>Created by Whitfield Diffie and Martin Hellman in 1976. </li></ul><ul><li>Also called asymmetric system. </li></ul><ul><li>Encryption key: public key </li></ul><ul><li>Decryption key: private key </li></ul>
    13. 13. Public Key Infrastructure
    14. 14. Idea behind Public Key <ul><li>B publishes design specs for a padlock </li></ul><ul><li>A wants to send B a box </li></ul><ul><li>A builds a B padlock, locks the box </li></ul><ul><li>B unlocks box using his key </li></ul><ul><li>E intercepts box, knows design specs </li></ul><ul><li>Goal: E still can’t build a key </li></ul><ul><li>Padlock = trapdoor one-way function </li></ul>
    15. 15. Public Key Cryptography <ul><li>A wants to talk to B: computes key X </li></ul><ul><li>A sends B f B ( X ) (B’s function) </li></ul><ul><li>B computes f B -1 ( f B ( X )) = X </li></ul><ul><li>Both A and B know X , use as key for symmetric encryption </li></ul><ul><li>E knows f B ( X ); can’t compute X </li></ul><ul><li>Asymmetric encryption </li></ul><ul><li>Whitfield Diffie, 1975 </li></ul>
    16. 16. Cryptanalysis Terms <ul><li>Clipertext – only attack – attacter-attempts to decrypt cliphertext. </li></ul><ul><li>Known-plaintext attack – attacter-attempts to decrypt cliphertext knowledge of some plaintext. </li></ul><ul><li>Chosen-plaintext attack – attacter-attempts obtains cliphertext corresponding to selected plaintext . </li></ul>
    17. 17. Crypto System Properties <ul><li>Encryption/decryption transformations must be efficient for all keys. </li></ul><ul><li>System must be easy to use. </li></ul><ul><li>The security of the system should depend ONLY on the secrecy of the keys and not on the secrecy of the encryption/decryption transformation. </li></ul>
    18. 18. Secrecy Requirements <ul><li>If cipher text and plaintext are known, it should be computationally infeasible to determine the deciphering algorithm. </li></ul><ul><li>It should be computationally infeasible to systematically determine plaintext from intercepted cipher text. </li></ul>
    19. 19. Authenticity Requirements <ul><li>If cipher text and plaintext are known, it should be computationally infeasible to determine the deciphering algorithm. </li></ul><ul><li>It should be computationally infeasible to find valid cipher text . </li></ul>
    20. 20. Digital Encryption Standard(DES) <ul><li>Developed by IBM in 1972. </li></ul><ul><li>Never approved for national security applications </li></ul><ul><li>64-bit plain & cipher text block size. </li></ul><ul><li>56-bit true key plus 8 parity bits. </li></ul><ul><li>Single chip implementation. </li></ul><ul><li>16 rounds transpositions & substitutions. </li></ul><ul><li>Symmetric , private key. </li></ul>
    21. 21. Applications of DES <ul><li>Double DES </li></ul><ul><li>Effective key length of 112 bits. </li></ul><ul><li>Work factor about the same as single DES. </li></ul><ul><li>Triple DES </li></ul><ul><li>encrypt with first key. </li></ul><ul><li>decrypt with second key. </li></ul><ul><li>encrypt with first key. </li></ul><ul><li>very secure. </li></ul>
    22. 22. How do We Encrypt? <ul><li>Protocol, or scheme: method of encryption </li></ul><ul><li>Cryptovariable, or key: secret information </li></ul>Symmetric encryption: decryption is the same cryptovariable ciphertext plaintext protocol
    23. 23. How could we break this? <ul><li>Case I: we don’t know the protocol </li></ul><ul><ul><li>Hard problem in cryptanalysis </li></ul></ul><ul><ul><li>“ Clark Kent” effect </li></ul></ul><ul><li>Case II: we know the protocol </li></ul><ul><ul><li>Need to guess the cryptovariable </li></ul></ul><ul><ul><li>Only 26 possibilities </li></ul></ul>
    24. 24. Substitution Cipher <ul><li>Allow any permutation of the alphabet </li></ul><ul><li>Key = permutation; 26! possibilities </li></ul><ul><li>26! = 403,291,461,126,605,635,584,000,000 </li></ul><ul><li>Roughly 2 88 : checking 1 billion per second, would take 12 billion years </li></ul><ul><li>Is there a better way? </li></ul><ul><li>Al-Kindi, ninth century: frequency analysis </li></ul>
    25. 25. The Perfect Cryptosystem <ul><li>One-time pad: encrypt each letter with its own key </li></ul><ul><li>-Example: Caesar shift each letter separately </li></ul><ul><li>C i = P i + K i (mod 26) </li></ul><ul><li>To encrypt n bits, use n bits of key </li></ul><ul><li>This uses up lots of key bits; need to prearrange </li></ul><ul><li>How do you generate key bits? </li></ul>
    26. 26. Enigma Machine <ul><li>German cryptosystem in World War II </li></ul><ul><li>Same idea: modify letters </li></ul><ul><li>Scrambler disks implement permutation </li></ul><ul><li>Rotate after each letter, so many different permutations used </li></ul><ul><li>Additional permutation provided by plugboard </li></ul>
    27. 27. Enigma Key <ul><li>Key changed daily </li></ul><ul><li>3 scramblers in one of 6 orders </li></ul><ul><ul><li>-In 1938: 3 of 5, so 60 arrangements </li></ul></ul><ul><li>26 3 = 17,576 settings for scramblers </li></ul><ul><li>Billions of plug board settings </li></ul><ul><li>Alan Turing: bypassed plug board </li></ul><ul><li>Used known plaintext, exhausted over space </li></ul><ul><li>British were able to read traffic </li></ul>
    28. 28. Modern Symmetric Cryptography <ul><li>Assume the protocol is known to the enemy </li></ul><ul><li>Only the key is secret </li></ul><ul><li>Encryption, cryptanalysis use computers </li></ul><ul><li>Operate on bits, rather than letters </li></ul><ul><li>DES, AES </li></ul><ul><li>Open standards; let everyone try to break it </li></ul><ul><li>Closed design often fails (cell phones) </li></ul>
    29. 29. Key Distribution <ul><li>Secure communication requires a key </li></ul><ul><li>How do you exchange keys securely? </li></ul><ul><li>Military: codebooks in field could fall into enemy hands </li></ul><ul><li>Commerce: might not meet face-to-face </li></ul><ul><li>Seems to be a Catch-22 </li></ul>
    30. 30. Paradigm Shift <ul><li>A wants to mail B a letter securely </li></ul><ul><li>If they share a “key”, A locks, B unlocks </li></ul><ul><li>If not: A puts on padlock, sends box to B </li></ul><ul><li>B adds his padlock, sends box back to A </li></ul><ul><li>A removes her padlock, sends box to B </li></ul><ul><li>B unlocks box, reads letter </li></ul><ul><li>Problem: how to translate this to mathematics </li></ul>
    31. 31. A, B agree on information Y A computes A(Y) Mails it to B B computes B(Y) Mails it to A Alcomputes A(B(Y)) B computes B(A(Y)) A(B(Y)) = B(A(Y)) = secret key “ E” knows Y, A(Y), B(Y), but can’t compute key Problem: how do you make A(B(Y)) = B(A(Y))?
    32. 32. Diffie-Hellman-Merkle (1976) <ul><li>Modular Arithmetic </li></ul><ul><li>Choose Y , modulus p </li></ul><ul><li>A’s function is Y A (mod p ) </li></ul><ul><li>B’s function is Y B (mod p ) </li></ul><ul><li>Key is Y AB  Y BA (mod p ) </li></ul><ul><li>E can’t compute Y AB from Y , Y A , Y B </li></ul><ul><li>We think (no one can prove it) </li></ul><ul><li>One problem: must communicate to get key </li></ul>
    33. 33. One-way Functions <ul><li>Easy to compute, hard to reverse </li></ul><ul><li>Example: f ( A ) = Y A (mod p ) </li></ul><ul><li>f -1 ( Y A ) is called “discrete log” </li></ul><ul><li>Hard to compute (we think) </li></ul><ul><li>Could always do exhaustive search </li></ul><ul><li>Here, there are p -1 choices </li></ul>
    34. 34. Cryptographic Primitives <ul><li>Building blocks for algorithms </li></ul><ul><ul><li>-Example: one-way functions </li></ul></ul><ul><li>Protocols built out of primitives </li></ul><ul><ul><li>-Example: Diffie-Hellman-Merkle </li></ul></ul><ul><li>Protocols built out of other protocols </li></ul><ul><ul><li>-Example: Use Diffie-Hellman to exchange key </li></ul></ul>
    35. 35. Trapdoor One-Way Functions <ul><li>Another useful primitive </li></ul><ul><li>f ( X ) is easy to compute </li></ul><ul><li>f -1 ( Y ) is hard for most people to compute </li></ul><ul><li>But: easy to compute if you know a secret </li></ul><ul><li>There are trapdoor one-way functions </li></ul><ul><li>Found by Rivest-Shamir-Adleman, 1977 </li></ul><ul><li>Rely on difficulty of factoring large integers </li></ul>
    36. 36. Digital Signature Scheme <ul><li>A wants to send B a message, sign it </li></ul><ul><li>A sends B X and S = f A -1 ( X ) </li></ul><ul><li>B checks that f A ( S ) = X </li></ul><ul><li>Therefore B knows that S = f A -1 ( X ) </li></ul><ul><li>Only A can compute f A -1 ( X ) easily, so A must have sent the message </li></ul><ul><li>Same primitive, new protocol </li></ul>
    37. 37. Digital Signature Process
    38. 38. Revolution <ul><li>New ideas made cryptography an option for commerce </li></ul><ul><li>PCs gave everyone computing power </li></ul><ul><li>Zimmerman’s PGP: gave everyone access </li></ul><ul><li>SSL in web browsers </li></ul>
    39. 39. Quantum Computation <ul><li>Computers revolutionized cryptographic design and cryptanalysis </li></ul><ul><li>Quantum computers may one day do the same </li></ul><ul><li>Quantum key exchange: guaranteed secure </li></ul><ul><li>A quantum computer could factor large integers in polynomial time </li></ul>
    40. 40. THANK YOU