Foundations of Cryptography
89-856
Yehuda Lindell
Dept. of Computer Science
Bar-Ilan University, Israel.
lindell@cs.biu.ac.il
April 26, 2010
c Copyright 2005 by Yehuda Lindell.
Permission to make copies of part or all of this work for personal or classroo

IITM-CS6111 Foundations of Cryptography
Assignment-1
Cryptosystem: Affine Cipher
Let P = C = Z26 and let
K = cfw_(a, b) Z26 Z26 : gcd(a, 26) = 1
For K = (a, b) K, define
eK (x) = (ax + b)
mod 26
and
dK (y) = a1 (y b)
mod 26
(x, y Z26 ).
1. (a) Prove that

IITM-CS6111 Foundations of Cryptography
Assignment-3
1. Prove that if there exists a one-way function, then there exists a one-way function
f such that f (0n ) = 0n for every n. Note that for infinitely many values y, it is easy
to compute f 1 (y). Why d

IITM-CS6111
Foundations of Cryptography
Assignment-2
1. Prove the following for random variables X, Y and Z :
(a) (X; Z) (X; Y ) + (X; Z).
P
(b) (X; Y ) = vV (Pr[X = v] Pr[Y = v]) with x y = max(x y, 0).
P
(c) (X; Y ) = 1 vV min(Pr[X = v], Pr[Y = v]).
2

Chapter 2
Homomorphic Encryption
Abstract Homomorphic encryption is a form of encryption which allows specific
types of computations to be carried out on ciphertexts and generate an encrypted
result which, when decrypted, matches the result of operations