Consider a “one-way” function h. Then, given the value y = h(x), it is computationally infeasible to find x directly from y.

a. Suppose that Alice computes y = h(x), where x is Alice’s salary, in dollars. If Trudy obtains y, how can she determine Alice’s salary xl

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Hint: Adapt the forward search attack to this problem.

b. Why does your attack not violate the one-way property of h?

c. How could Alice prevent this attack ? We assume that Trudy has access to the output of the function h, Trudy knows that the input includes Alice’s salary, and Trudy knows the format of the input. Also, no keys are available, so Alice cannot encrypt the output value.

Suppose that Alice uses a stream cipher to encrypt plaintext P, obtaining ciphertext C, and Alice then sends C to Bob. Suppose that Trudy happens to know the plaintext P, but Trudy does not know the key K that was used in the stream cipher.

a. Show that Trudy can easily determine the keystream that was used to encrypt P.

b. Show that Trudy can, in effect, replace P with plaintext of her choosing, say, P’. That is, show that Trudy can create a ciphertext message C” so that when Bob decrypts C’ he will obtain P’.

Suppose that a particular cipher uses a 40-bit key, and the cipher is secure (i.e., there is no known shortcut attack).

a. How much work, on average, is an exhaustive search attack?

b. Outline an attack, assuming that known plaintext is available.

c. How would you attack this cipher in the ciphertext-only case?

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