Question

A cryptographic hash takes a message as input and produces a fixed-length string as output, called the digital fingerprint. A brute force attack involves computing the hash for a large number of messages until a pair of distinct messages with the same hash is found. Find the number of attempts required so that the probability of obtaining a match is How many attempts are required to find a matching pair if the digital fingerprint is 64 bits long? 128 bits long?

Answer 1

Answer:

$1.85x10^{19}$ attempts are required to find a matching pair if the digital fingerprint is 64 bits long.

$3.40*10^{38}$ attempts are required to find a matching pair if the digital fingerprint is 128 bits long.

Step-by-step explanation:

Each bit has two options. So

How many attempts are required to find a matching pair if the digital fingerprint is 64 bits long?

So for each of the 64 bits, we have the following number of options.

2 - 2 - 2 - 2 -... - 2

So, in all, there are

$T = 2^{64} = 1.85x10^{19}$

options.

So, $1.85x10^{19}$ attempts are required to find a matching pair if the digital fingerprint is 64 bits long.

128 bits long?

Using the same logic as the first question.

$T = 2^{128} = 3.40*10^{38}$

So, $3.40*10^{38}$ attempts are required to find a matching pair if the digital fingerprint is 128 bits long.