Name Deven Puri
Machine Invictus
ip 10.129.30.16

Assignment 1


Problem Statement:

A terrorist transmits the same message m to each of his 3 accompliers across the globe. The accomplies have different
 private keys (d1, n1), (d2, n2) and (d3, n3). They have the same encryption key 3. Further, n1, n2 and n3 are
 relatively prime to each other.
The terrorist encrypts the message m before transmission. All the three encrypted messages, c1, c2 and c3, are
 intercepted during transmission.Show how to recover m without being able to factorize n1, n2 or n3.



Solution:

we have 
M^3 mod n1=c1
M^3 mod n2=c2
M^3 mod n3=c3

we require M

Using Chinese remainder theorm we can find M^3 mod N(=n1*n2*n3) see SECTION 1.1 for proof
take cube root of (M^3 )modulo N.

Well one might argue take cube root of M^3 mod n1 or M^3 mod n2 or M^3 mod n3!!!!!!!!!!!!!!!!!!
Is the problem equally Hard 



  
