2. Block Cipher Given a two-key triple encryption for block cipher. Let F be a block cipher with n-bit block def length and key length, and set Fx1,k(x) Fky (Fk?! (Fk (x)). (a) Assume that given a pair (m, m2) it is possible to find in constant time all keys k2 such that m2 = F2 (m). Show how to recover the entire key for F' (with high probability) in time roughly 2" using three known input/output pairs. (b) In general, it will not be possible to find k2 as above in constant time. However, show that by using a pre-processing step taking 21 time it is possible, given m2, to find in (essentially) constant time all keys k2 such that m2 = F (on). (c) Assume ki is known and that the pre-processing step above has already been run. Show how to use the value y = FX1,52 (2) for a single chosen plaintext x to determine ka in constant time. (d) Put the above components together to devise an attack that recovers the entire key of F by running in roughly 2n time and requesting the encryption of roughly 2n chosen inputs. 2. Block Cipher Given a two-key triple encryption for block cipher. Let F be a block cipher with n-bit block def length and key length, and set Fx1,k(x) Fky (Fk?! (Fk (x)). (a) Assume that given a pair (m, m2) it is possible to find in constant time all keys k2 such that m2 = F2 (m). Show how to recover the entire key for F' (with high probability) in time roughly 2" using three known input/output pairs. (b) In general, it will not be possible to find k2 as above in constant time. However, show that by using a pre-processing step taking 21 time it is possible, given m2, to find in (essentially) constant time all keys k2 such that m2 = F (on). (c) Assume ki is known and that the pre-processing step above has already been run. Show how to use the value y = FX1,52 (2) for a single chosen plaintext x to determine ka in constant time. (d) Put the above components together to devise an attack that recovers the entire key of F by running in roughly 2n time and requesting the encryption of roughly 2n chosen inputs