Problem 1 Symmetric encryption with a deck of cards. Alice shuttles a
deck of cards and deals it all out to herself and Bob (each of them gets half of
the 52 cards). They do not share any keys. Alice now wishes to send a secret
message Mto Bob by showing something (probably very very long) publicly.
Eavesdropper Eve is listening in: she can see everything Alice shows, but
Eve can’t see the cards.
Suppose we want to achieve perfect secrecy; that is, Eve has no informa-
tion at all about what is M. What is the maximum number of bits Mcan
be in this scheme.
Problem 2 The following two keys enhancements to DES were proposed
in order to increase the complexity of finding the keys by exhaustive search.
Letusdenotethemas:
DESXk,k1(M)=DESk(M)⊕k1,(1)
DESYk,k1(M)=DESk(M⊕k1)(2)
The key length is |k|=56and|k1|=64(k1is 64 bits because the block
size for DES is 64 bits. Show that both these proposals do not increase
the complexity of breaking the cryptosystem using brute-force key search.
That is, the number of DES encryptions/decryptions is still in the order of
256. You can assume that you can have a moderate number of plaintext-
ciphertext pairs.
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