ps6 - ing an adversary A such that Adv ind-cpa AE A is high...

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Computer Science and Engineering, UCSD Spring 11 CSE 207: Modern Cryptography Instructor: Mihir Bellare Problem Set 6 May 11, 2011 Problem Set 6 Due: Wednesday May 18, 2011, in class. Problem 1. [35 points] Let p 3 be a prime and g Z * p a generator of Z * p . (These are public quantities, known to all parties including the adversary.) Consider the key-generation and encryption algorithms below: Algorithm K x $ Z * p - 1 X g x mod p return ( X,x ) Algorithm E ( X,M ) if M n∈ Z * p then return y $ Z p - 1 ; Y g y mod p Z X y mod p ; W Y · M mod p return ( Z,W ) The message space associated to public key X is Messages ( X ) = Z * p . We let k be the bit-length of p . 1. [15 points] Specify a decryption algorithm D such that AE = ( K , E , D ) is an asymmetric encryption scheme satisfying the correct decryption property. State the running time of your algorithm as a function of k (the lower this is, the more credit you get) and prove that the correct decryption property holds. 2. [20 points] Show that this scheme is insecure with regard to the ind-cpa property by present-
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Unformatted text preview: ing an adversary A such that Adv ind-cpa AE ( A ) is high. You should specify the adversary, state its running time as a function of k (the smaller this is, the more credit you get), state the value of its advantage (the larger this is, the more credit you get) and justify the correctness of the adversary. Problem 2. [30 points] Let AE = ( K , E , D ) be an asymmetric encryption scheme whose message space includes { , 1 } k . DeFne the KEM KEM = ( K , EK , D ) with keylength k via algorithm EK K $ ← { , 1 } k C $ ← E pk ( K ) return ( K,C ) Show that if AE is IND-CCA secure, then so is KEM . This means you must state a reduction-style theorem and then prove it. The better your bounds, the more points you get. 1...
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