06 - Statistical and Introduction Computational 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 Statistical Security Let X and Y be two distributions over The statistical distance between X and Y , denoted ( X , Y ) is A symmetric encryption scheme is said to be ε -statistically secure, if for any two plaintexts distributions are ε -equivalent 2 1 , P P ) ( ), ( 2 1 P E P E k k | ] Pr[ ] Pr[ | max } 1 , 0 { T T m T - Y X m } 1 , 0 {
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Cryptography and Protocols – Computational Security 6-3 Algorithms Algorithm Algorithm performs a sequence of `elementary steps’ that can be: - arithmetic operations - bit operations - Turing machine moves - ………. (but not quantum computing!!) We allow probabilistic algorithms, that is flipping coins is permitted algorithm input output 0001101100111 10100110111
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Cryptography and Protocols – Computational Security 6-4 Complexity The time complexity of algorithm A is function f(n) that is equal to the number of elementary steps required to process the most difficult input of length n We do not distinguish algorithms of complexity 2n² and 100000n² A computational problem has time complexity at most f(n) if there is an algorithm that solves the problem and has complexity O(f(n)) - problem solvable in linear time: there is an algorithm that on input of length n performs at most Cn steps - problem solvable in quadratic time: there is an algorithm that on input of length n performs at most Cn² steps Polynomial time solvable problems: O(polynomial); P, BPP
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Cryptography and Protocols – Computational Security 6-5 Complexity (cntd) Polynomial time solvable problems: There is a polynomial p(n) such that the problem is solvable in time O(p(n)
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06 - Statistical and Introduction Computational Security...

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