Question 1

Answer 1

Given:

2000 bits message is used to produce 256 bits hash

The number of different message which can be produce are  = 2²⁰⁰⁰

The number of different hash which can be produce = 2²⁵⁶

Hence the average number of messages having same hash = 2²⁰⁰⁰/2²⁵⁶ = 2^{2000 – 256} = 2¹⁷⁴⁴

Thus above result state that to have unique hash value for different message the length of message must be approximately equal or less than the length of hash.