Question: No , the scheme does not have CPA security either. Distinguisher ( identical to CPA$ ) : The same distinguisher from ( a ) can
No the scheme does not have CPA security either.
Distinguisher identical to CPA$: The same distinguisher from a can be used to attack CPA security as well. The distinguisher can query the encryption oracle for any message and check for divisibility by to learn information about the encrypted message.
Advantage: The distinguisher's advantage remains significantly greater than
If c is divisible by it implies the padding scheme successfully created a prime number with a trailing zero. This has a nonnegligible probability of occurring, especially for smaller message lengths.
If c is not divisible by it means the padding scheme failed to produce a prime number with a trailing zero, suggesting a different message was encrypted.
Key Point:
The fundamental flaw lies in the predictability of the padding scheme. Knowledge of the padding scheme's structure allows an attacker to glean information about the message by examining ciphertext properties divisibility by in this case
st step:
The encryption scheme is not CPA secure because an attacker can determine if a message is encrypted by checking if the ciphertext is divisible by This is because the padding scheme always adds a trailing zero to the message before encrypting it If the ciphertext is divisible by then the attacker knows that the message was encrypted with the padding scheme. Otherwise, the attacker knows that the message was encrypted with a different scheme.
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