COMP-547 2017 Homework set #2 Due Wednesday February 15, 2017 23:59

Exercises from Katz and Lindell’s book(1.1, 1.5, 1.6, 1.7, 2.8, 2.9, 2.13)

Historic Cryptography

Let (Gen1,Enc1,Dec1), (Gen2,Enc2,Dec2), and (Gen3,Enc3,Dec3) be three encryption schemes over the same message space M. Consider the composed encryption scheme (Genc,Encc,Decc) over message space M defined as

Genc = (Gen1,Gen2,Gen3)

Encc(m) = pick at random u,v∈M; return ( Enc1(u), Enc2(v), Enc3(u⊕v⊕m) )

Decc(u,v,w) = return ( Dec1(u) ⊕ Dec2(v) ⊕ Dec3(w) )

Prove that if any of the three encryption schemes (Gens,Encs,Decs), 1≤s≤3, is perfectly secret then so is (Genc,Encc,Decc).

Perfect Secrecy

[10%]

[15%]

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[5%]

[10%]

[15%]

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[10%]