# 05 - Statistical and Introduction Computational Security Cryptography and Protocols Andrei Bulatov Cryptography and Protocols Statistical Security

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Introduction Statistical and Computational Security Cryptography and Protocols Andrei Bulatov

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Cryptography and Protocols – Statistical Security 5-2 Symmetric Encryption Scheme A symmetric encryption scheme is a triple of algorithms (K,E,D) - K keys generation - E encryption algorithm - D decryption algorithm For simplicity assume that k K uniformly at random, or plaintext In general, E (and possibly D) are randomized l k } 1 , 0 { l U k m P } 1 , 0 { C P E E k m l = × ) ( | } 1 , 0 { } 1 , 0 { } 1 , 0 { : * P C D D k m l = × ) ( | } 1 , 0 { } 1 , 0 { } 1 , 0 { : *
Cryptography and Protocols – Statistical Security 5-3 Perfect Security Let (K,E,D) be a symmetric encryption scheme. It is said to be perfectly secure if for any two plaintexts and a ciphertext C where the probability is over the random choice k K, and also over the coins flipped by E ], ) ( Pr[ ] ) ( Pr[ 2 1 C P E C P E k k = = = 2 1 , P P

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X Y 000 001 010 011 100 101 110 111 Let X and Y be two distributions over The statistical distance between X and Y , denoted ( X , Y ) is Cryptography and Protocols – Statistical Security 5-4 Statistical Distance | ] Pr[ ] Pr[ | max } 1 , 0 { T T m T - Y X m } 1 , 0 { T If ( X , Y ) ≤ ε we write Y X ε
Cryptography and Protocols – Statistical Security 5-5 Statistical Security A symmetric encryption scheme is said to be ε -statistically secure, if for any two plaintexts distributions are ε -equivalent Theorem .

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## This note was uploaded on 03/05/2012 for the course CMPT 404 taught by Professor Andreia.bulatov during the Spring '12 term at Simon Fraser.

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05 - Statistical and Introduction Computational Security Cryptography and Protocols Andrei Bulatov Cryptography and Protocols Statistical Security

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