homework 2 - ICS 180 Introduction to Cryptography Homework...

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ICS 180: Introduction to Cryptography 4/15/2004 Homework 2 Due Thursday, 4/22/2004 at the beginning of class. 1 Security Definitions [10+20 points] Definition of some security property often goes like this: We call some communication scheme Σ secure in the sense of resistance against attack of type “X” if for all probabilistic polynomial time algorithms A , the probability that A succeeds in an “attack of type X” against Σ is negligibly small, i.e. it’s a negligible function of the security parameter τ . For example, the definition of one-way secure encryption scheme Σ = ( KGen, Enc, Dec ) has exactly this form, where “attack of type X” of A against Σ is the “decryption attack”, defined as follows: (1) KGen is executed on the security parameter τ to create key k , (2) random m is picked in the messages space M , (3) ciphertext c is computed as Enc ( k, m ), and finally (4) A runs on input c and outputs some string m . We say that A succeeds in this attack if m = m . 1.1 [10 points] Show a (trivial) PPT algorithm which succeeds with a non-zero but negligible probability in an attack against the “one way security” property of the one-time pad encryption scheme defined for message space M = { 0 , 1 } τ and key space K = { 0 , 1 } τ , where τ is the security parameter. Note that this means that even if a scheme is perfectly secure , let alone one-way secure , there nevertheless usually exist efficient attacks against it which succeed with negligible probability. This, in part, is why we usually cannot ask that that the probability of suc- cessful break of our scheme be zero for all efficient algorithms.
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