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Slide 6 Direct proof: Construct adversary A as follows: Mo = ( 0 ' , 0 ) and M , = ( 0 ' ,
Slide
Direct proof:
Construct adversary A as follows:
Mo and M
Challenge ciphertext C G
Adversary A: if Cthen belse b
If bthen b
If bthen b
So bbwith probability
THEOREM
If Enc is deterministic and stateless the encryption scheme cannot satisfy definition
Slide
The multiplemessage eavesdropping experiment PrivKA, n:
The adversary A is given input and outputs a pair of
equallength lists of messages Mo momotand M
MMtwith moi mil for all i
A key k is generated by running Genand a uniform bit bE is chosen. For all ithe ciphertext ci Ench mbiis computed and the list CCCtis given to A
A outputs a bit b
The output of the experiment is defined to be if band
O otherwise.
DEFINITION A privatekey encryption scheme II GenEnc Dec
has indistinguishable multiple encryptions in the presence of an eavesdropper if for all probabilistic polynomialtime adversaries A there is a negligible function negl such that
Pr PrivKAHn
negln
Question
Consider the following statement: Theorem slide establishes that a necessary and sufficient condition for an encryption scheme to satisfy Definition slide is that the Enc algorithm of be randomized or stateful. Discuss.
Slide
Suppose Fkfor any k
Then D will always output
PrDFK
Question
In Example slide we have the following claim
Suppose O Fk for any k
Then D will always output
Explain why this claim is true.
Slide
The CPA indistinguishability experiment PrivKA,n:
n:
A key k is generated by running Gen
The adversary A is given input and oracle access to Enckand outputs a pair of messages momy of the same length.
A uniform bit b e is chosen, and then a ciphertext c Enckmbis computed and given to A
The adversary A continues to have oracle access to Enckand outputs a bit
The output of the experiment is defined to be if bband
O otherwise. In the former case, we say that A succeeds.
DEFINITION A privatekey encryption scheme II GenEnc Dec
has indistinguishable encryptions under a chosenplaintext attack, or is CPAsecureif for all probabilistic polynomialtime adversaries A there is a negligible function negl such that
Pr PrivKAan
negln
where the probability is taken over the randomness used by Aas well as the randomness used in the experiment.
Let qnbe a polynomial upper bound on number of queries A makes to the oracle
Question
Slide introduces the notation Let qnbe a polynomial upper bound on number of queries A makes to the oracle.Does a PPT adversary A satisfy this requirement? Explain.
Slide
CONSTRUCTION
Let F be a pseudorandom function. Define a fixedlength, privatekey encryption scheme for messages of length n as follows:
Gen: on input choose uniform k and output it
Enc: on input a key k and a message m choose uniform r E and output the ciphertext
c:rFkrem
Dec: on input a key k E and a ciphertext c rsoutput the message
m:Fkr@s
A CPAsecure encryption scheme from any pseudorandom function.
Question
In context of construction slide let nso the encryption scheme can be used to encrypt a message of length bits How many possible ciphertexts exist for a single plaintext message and a fixed key kExplain
Plz ans by thank you
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