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Assume ƒUUÀœüpeach encipherment takes 1 time unit. A cryptanalyst will use a known plaintext attack to determine the key from …*¨À¨û@two messages  Ím ã0 Ê,  Ím ã1 Ê and their corresponding ciphertexts  Íc ã0 Ê and  Íc ã1 Ê. xÀ¼UM €The cryptographer computes  ÍE âx Ê( Ím ã0 Ê) for each possible key  Íx Ê and stores each in a table. How many bits of ƒUUÀÊ*Ÿ@Rmemory does the table require? How many time units does computing the entry take? y…*¨ÀÙ*ž €&She then computes  Íy Ê =  ÍD âxÕ Ê( Íc ã0 Ê), where  ÍD Ê is the decipherment function corresponding to  ÍE Ê, for each possible ƒUUÀæÿð€key  ÍxÕ Ê. She then checks the table to see if  Íy Ê is in it.. If so, ( Íx Ê,  ÍxÕ Ê) is a candidate for the key pair. How should 0Àòÿï~the table be organized to allow the cryptographer to find a match for  Íy Ê in time  ÍO Ê(1)? How many time units @&would pass before a match must occur? zÁ ÿí`fHow can the cryptographer confirm that ( Íx Ê,  ÍxÕ Ê) is in fact the key pair she seeks? {`aWhat is the maximum time and memory needed for the attack? What is the expected time and memory? |Á.ÿë €( Í20 points Ê) A network consists of  Ín Ê hosts. Assuming cryptographic keys are distributed on a per-host-pair basis, Á:ÿê@5please compute how many different keys are required. }…*¨ÁLÿé €( Í40 points Ê) Consider an RSA digital signature scheme. Alice tricks Bob into signing messages  Ím ã1 Ê and  Ím ã2 Ê such PÁZÕ;@€that  Ím Ê =  Ím ã1 Ím ã2 Ê mod  Ín âBob Ê. Prove that Alice can forge BobÕs signature on  Ím Ê. 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