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[Insecure PRF) Let F be a secure PRF. Let X denote a bitwise complement of the string x. Define a new function F'(k,x) = F(k,x)

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[Insecure PRF) Let F be a secure PRF. Let X denote a bitwise complement of the string x. Define a new function F'(k,x) = F(k,x) || F(k,x), where "I" denotes concatenation. Show that F' is not a secure PRF. Hints and tips: Construct an adversary that distinguishes F from a random function. Remember that by the definition of PRF, an adversary is allowed to query PRF on arbitrary inputs. Remember that under a fixed key k, any PRF returns the same outputs when queried on the same inputs-you may apply this observation to F. [Insecure PRF) Let F be a secure PRF. Let X denote a bitwise complement of the string x. Define a new function F'(k,x) = F(k,x) || F(k,x), where "I" denotes concatenation. Show that F' is not a secure PRF. Hints and tips: Construct an adversary that distinguishes F from a random function. Remember that by the definition of PRF, an adversary is allowed to query PRF on arbitrary inputs. Remember that under a fixed key k, any PRF returns the same outputs when queried on the same inputs-you may apply this observation to F

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