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# crypto1-2n - Cryptography Outline 15-853:Algorithms in the...

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1 15-853 Page 1 15-853:Algorithms in the Real World Cryptography 1 and 2 15-853 Page 2 Cryptography Outline Introduction: terminology, cryptanalysis, security Primitives: one-way functions, trapdoors, … Protocols: digital signatures, key exchange, . . Number Theory: groups, fields, … Private-Key Algorithms: Rijndael, DES Public-Key Algorithms: Knapsack, RSA, El-Gamal, … Case Studies: Kerberos, Digital Cash 15-853 Page 3 Cryptography Outline Introduction: –te rm ino logy – cryptanalytic attacks –secu r i ty Primitives: one-way functions, trapdoors, … Protocols: digital signatures, key exchange, . . Number Theory: groups, fields, … Private-Key Algorithms: Rijndael, DES Public-Key Algorithms: Knapsack, RSA, El-Gamal, … Case Studies: Kerberos, Digital Cash 15-853 Page 4 Some Terminology Cryptography – the general term Cryptology –the mathemat ics Encryption – encoding but sometimes used as general term) Cryptanalysis –break ing±codes Steganography – hiding message Cipher – a method or algorithm for encrypting or decrypting

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2 15-853 Page 5 More Definitions Private Key or Symmetric : Key 1 = Key 2 Public Key or Asymmetric : Key 1 Key 2 Key 1 or Key 2 is public depending on the protocol Encryption Decryption Key 1 Key 2 Cyphertext E k (M) = C D k (C) = M Original Plaintext Plaintext 15-853 Page 6 Cryptanalytic Attacks C = ciphertext messages M = plaintext messages Ciphertext Only: Attacker has multiple C s but does not know the corresponding M s Known Plaintext: Attacker knows some number of (C,M) pairs. Chosen Plaintext: Attacker gets to choose M and generate C . Chosen Ciphertext: Attacker gets to choose C and generate M . 15-853 Page 7 What does it mean to be secure? Unconditionally Secure : Encrypted message cannot be decoded without the key Shannon showed in 1943 that key must be as long as the message to be unconditionally secure – this is based on information theory A one time pad – xor a random key with a message (Used in 2 nd world war) Security based on computational cost : it is computationally “infeasible” to decode a message without the key. No (probabilistic) polynomial time algorithm can decode the message. 15-853 Page 8 The Cast Alice – initiates a message or protocol Bob - second participant Trent – trusted middleman Eve –eavesdropper Mallory – malicious active attacker Trent Alice Bob Eve Mallory
3 15-853 Page 9 Cryptography Outline Introduction: terminology, cryptanalysis, security Primitives: – one-way functions – one-way trapdoor functions – one-way hash functions Protocols: digital signatures, key exchange, . . Number Theory: groups, fields, … Private-Key Algorithms: Rijndael, DES Public-Key Algorithms: Knapsack, RSA, El-Gamal, … Case Studies: Kerberos, Digital Cash 15-853 Page 10 Primitives: One-Way Functions (Informally): A function Y = f(x) is one-way if it is easy to compute y from x but “hard” to compute y Building block of most cryptographic protocols And, the security of most protocols rely on their existence.

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crypto1-2n - Cryptography Outline 15-853:Algorithms in the...

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