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below is a exercise question in the book A Graduate Course in Applied Cryptography, can somebody help me with the answer? 6.5 (MA C combiners).

below is a exercise question in the book "A Graduate Course in Applied Cryptography", can somebody help me with the answer?

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6.5 (MA C combiners). We want to build a MAC system I using two MAC systems I1=(S1,V1) and I2=(S2,V2), so that if at some time one of I1 or I2 is broken (but not both) then I is still secure. Put another way, we want to construct I from I1 and I2 such that I is secure if either I1 or I2 is secure. (a) Define I=(S,V), where S((k1,k2),m):=(S1(k1,m),S2(k2,m)), and V is defined in the obvious way: on input (k,m,(t1,t2)),V accepts iff both V1(k1,m,t1) and V2(k2,m,t2) accept. Show that I is secure if either I1 or I2 is secure. 244 (b) Suppose that I1 and I2 are deterministic MAC systems (see the definition on page 214), and that both have tag space {0,1}n. Define the deterministic MAC system I=(S,V), where S((k1,k2),m):=S1(k1,m)S2(k2,m). Show that I is secure if either I1 or I2 is secure

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