CSE 5351 Homework 1
Due: Wednesday, January 23 by class time
1. Consider the Caesar Cipher: M K C cfw_0, 1, 2, , 25 and Enc k ( m= m + k mod 26.
Suppose Pr( m) = S and Pr( k ) = S for all m M and k K , where
( m + 1)
( k + 1)
S = 1 + 2 + 3 + + 26 = 35
CSE 5351 Homework 2
Due: Wednesday, January 30 by class time
1. Consider an encryption scheme (G,E,D). Show that if the encryption algorithm E is
deterministic (rather than probabilistic), then it cannot be computationally multipleciphertext indistinguish
CSE 5331 Homework 3
Due: Monday, February 11 by class time
1. In the definition of computationally single-ciphertext-indistinguishable against
eavesdroppers (slides 28, 29), the adversary is required to output two messages of the same
length. Prove that i
CSE 5351 Homework 4
Due: Monday, February 18 by class time
1. Let G be a pseudorandom generator with expansion factor l (n) = 2n. Define
f k ( x) =) for k cfw_0,1n and x cfw_0,12 n . Is
x G (k
: k cfw_0,1n a family of
pseudorandom functions? Just
CSE 5351 Homework 5
Due: Wednesday February 27, by class time
Midterm exam: Monday, March 4th. Open-notes, closed book.
Scope: up to Hash and MAC (inclusive).
1. Let cfw_ f k :cfw_0,1n cfw_0,1n
be a family of n-bit pseudorandom functions.
CSE 5351 Homework 6
Due: Wednesday March 20 by class time
1. Fix the RSA modulus n, and assume there is an adversary A running in time t for which
Pr A ( x e mod N ) =x : x u Z N =0.01.
That is, A can decrypt the ciphertext of a random message x with pr
CSE 5351 Homework 7
Due: Wednesday, April 3 by class time
Late homework will not be accepted.
1. Assume that Alice's RSA keys are ( n1 , e1 , d1 ) , and Bob's are ( n2 , e2 , d 2 ) . Suppose Alice
generates a signed and encrypted message by:
c := ( m d1 m