(1) Consider the extension of the One-time Pad cipher, where a ciphertext c is possibly longer...

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(1) Consider the extension of the One-time Pad cipher, where a ciphertext c is possibly longer than the plaintext m (and the key k) by one bit, namely, by having the encryption algorithm Enc appending to mk, either a 0 with probability 0.65 or a 1 with probability 0.3. Is this extension a perfectly secret cipher and why? (2) Based on your answer in the previous question, prove or refute the following statement: An encryption scheme with message space M is perfectly secret if and only if for every probability distribution DM over M and every co, c₁ E C we have Pr[C= co] Pr[C = c₁]. = (3) Consider the following encryption scheme. The message space is M = {m = {0, 1}| the last bit of m is 0}, algorithm Gen chooses a uniform key from {0,1}-¹, algorithm Enck (m) returns ciphertext m © (k||0), and algorithm Decê (c) returns c ℗ (k||0). Is this a perfectly secret cipher and why? (4) When the One-time Pad encryption algorithm runs with the all-zero key k = 0, the resulted ciphertext c equals the plaintext m. Consider the extension that purposely avoids this situation by disallowing Gen choosing the all-zero key-that is, k is chosen uniformly at random from the set of nonzero binary strings of length l. Is this extension a perfectly secret cipher and why? (1) Consider the extension of the One-time Pad cipher, where a ciphertext c is possibly longer than the plaintext m (and the key k) by one bit, namely, by having the encryption algorithm Enc appending to mk, either a 0 with probability 0.65 or a 1 with probability 0.3. Is this extension a perfectly secret cipher and why? (2) Based on your answer in the previous question, prove or refute the following statement: An encryption scheme with message space M is perfectly secret if and only if for every probability distribution DM over M and every co, c₁ E C we have Pr[C= co] Pr[C = c₁]. = (3) Consider the following encryption scheme. The message space is M = {m = {0, 1}| the last bit of m is 0}, algorithm Gen chooses a uniform key from {0,1}-¹, algorithm Enck (m) returns ciphertext m © (k||0), and algorithm Decê (c) returns c ℗ (k||0). Is this a perfectly secret cipher and why? (4) When the One-time Pad encryption algorithm runs with the all-zero key k = 0, the resulted ciphertext c equals the plaintext m. Consider the extension that purposely avoids this situation by disallowing Gen choosing the all-zero key-that is, k is chosen uniformly at random from the set of nonzero binary strings of length l. Is this extension a perfectly secret cipher and why?

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Extension of Onetime Pad This extension is not a perfectly secret cipher In a perfectly secret ciphe... View the full answer