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Problem 1 : On leaking, or hiding, the message length Consider encryption scheme Gen, Enc, Dec ) that is EAV - secure w . r

Problem 1: On leaking, or hiding, the message length
Consider encryption scheme Gen, Enc, Dec) that is EAV-secure w.r.t. the definition in Figure 1.
Figure 1: Indistinguishability of encryptions in the presence of an eavesdropper.
(3) Show that EAV2-security can be achieved by encryption schemes defined over messages up to
a given maximum length, i.e., by schemes ' such that for kin{0,1}n, algorithm Enc ?k' is defined
over message space M'={m:|m|l}, where ll(n) for some given polynomial l(*).
Hint: Construct a scheme '=(Gen',Enc',Dec') that encrypts messages in M' by
employing a EAV-secure scheme Gen, Enc, Dec) with message space M. Consider
an algorithm Enc ?' that on input message m'inM', merely applies Enc on a unique
and inversible encoding m=E(m')inM of m' in a way that "compensates" for the
absence of the restriction |m0|=|m1| in game PrivK-EAV2A,'(n). Then, prove that '
is EAV2-secure via a proof by reduction.
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