E:(k,m) = ( E(k,m), E(k,m)) = (C1,C₂) ; D₂=(K, (C₁,C₂)) = D(k,c₁), if D(k,c₁) = D(K, C₂) reject otherwise
E:(k,m) = ( E(k,m), E(k,m)) = (C1,C₂) ; D₂=(K, (C₁,C₂)) = D(k,c₁), if D(k,c₁) = D(K, C₂) reject otherwise
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Your Question:
Let (E,D) be an AE-secure cipher (remember that AE = authenticated encryption).
Show that the following derived cipher is not AE-secure where k is the key:
Description: D(k,c if D(k,c) D(k,ca) reject otherwise
Hints: Remember that AE-security implies chosen-ciphertext security. Also, note that the encryption algorithm “E” is probabilistic, and therefore each computation of “E(k,m)” (as in the above scheme) results in a different ciphertext (with overwhelming probability), and therefore we have c1 ? c2 with overwhelming probability.

Transcribed Image Text:E:(k,m) = ( E(k,m), E(k,m)) = (C1,C₂)
; D₂=(K, (C₁,C₂)) =
D(k,c₁), if D(k,c₁) = D(K, C₂)
reject otherwise
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