Let F be a PRF with K = X = Y = {0, 1}n. Let G be a PRG s.t. |G(x)| = 2|x|, e.g.

Question

Let F be a PRF with K = X = Y = {0, 1}n. Let G be a PRG s.t. |G(x)| = 2|x|, e.g. G expands an l-bit seed into a 2l-bit string. For each encryption scheme below, state whether it is (a) indistinguishable, and (b) CPA-secure, and briefly justify your answers. Let M = {0, 1}4(n + 1), and let E(k, m) = (G([k|0]) m1, G([k|l]) m2) where m = [m1 | m2] for m1, m2 {0, l}2(n + 1). Let M = {0, l}4n, and let E(k,m) = G([k | k]) m. Let M = {0, l}2n, and let E(k,m) = (r,G(r) m) for a random r in {0, 1}n. Let M = {0, 1}n, and let E(k, m) = F(k, 1n) m. Let M = {0, 1}n, and let E(k, m) = F(k, k) m.

Explanation / Answer

(a) indistinguishable (b)cpa secure (c)cpa secure (d)cpa secure (e)cpa secure

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