Question

*Password entropy is a measure of the predictability of a computer password. The higher the entropy, the more difficult it is to guess the password. The relationship between the password entropy, p. (measured in bits) and the number of guesses, G, required to decode the password is given by 0.301p = log,, G (a) Calculate the value of p for a password that takes 5000 guesses to decode. (b) Write down G as a function of p. (c) Find the number of guesses required to decode a password that has an entropy of 28 bits. Write your answer in the form a x 10', where I Sa<10, ke Z There is a point on the graph of the function G(p) with coordinates (0, 1). (d) Explain what these coordinate values mean in the context of computer passwords

Answer 1

The relationship between password entropy and the number of guesses required to decode a password is given by 0.301p = log(G). To calculate the value of p for a password that takes 5000 guesses to decode, rearrange the equation and solve. To write down G as a function of p, rearrange the equation. To find the number of guesses required to decode a password with a given entropy, substitute the entropy value into the equation. The coordinate values (0, 1) mean that a password with no entropy is extremely easy to guess, as it only requires 1 guess.

Step-by-step explanation:

The relationship between password entropy p (measured in bits) and the number of guesses G required to decode the password is given by the equation 0.301p = log(G).

(a) To calculate the value of p for a password that takes 5000 guesses to decode, we need to rearrange the equation to solve for p. Divide both sides of the equation by 0.301 to get p = log(G) / 0.301. Substitute G = 5000 into the equation to get p = log(5000) / 0.301. Use a calculator to find the approximate value of p.

(b) To write down G as a function of p, we need to rearrange the equation. Take the exponent of both sides to get G = e^(0.301p). This is the function that relates the number of guesses G to the password entropy p.

(c) To find the number of guesses required to decode a password with an entropy of 28 bits, substitute p = 28 into the equation G = e^(0.301p). Use a calculator to find the approximate value of G.

(d) The coordinate values (0, 1) represent the password entropy p = 0 bits (no entropy) and the number of guesses G = 1. In the context of computer passwords, this means that a password with no entropy is extremely easy to guess, as it only requires 1 guess.

Answer 2

To calculate the password entropy p for 5000 guesses, the formula 0.301p = log10(G) gives p as 12.29 bits. G expressed as a function of p is G = 10^(p/0.301), and for a 28-bit entropy, the number of guesses required is approximately 9 x 10^92. The point (0, 1) suggests a 0-bit entropy password needs just 1 guess.

Step-by-step explanation:

Password entropy is a measure of how unpredictable a password is, essentially indicating its strength against being guessed or cracked. A higher value of entropy suggests a more secure password.

Calculating Entropy (p) for a Given Number of Guesses

To calculate the entropy for a password that requires 5000 guesses to decode, we use the formula 0.301p = log10(G). We plug in G = 5000 and solve for p:

0.301p = log10(5000)
0.301p = log10(5 x 10^3)
0.301p = log10(5) + log10(10^3)
0.301p = 0.6990 + 3
0.301p = 3.6990
p = 3.6990 / 0.301
p = 12.29 bits approximately

G as a Function of p

To express G as a function of p, we rearrange the formula to G = 10^(p/0.301).

Number of Guesses for Entropy of 28 bits

For an entropy of 28 bits, we calculate:
G = 10^(28/0.301)
G = 10^92.99
G is approximately 9 x 10^92.

Meaning of the Coordinates (0, 1)

The point (0, 1) on the graph of function G(p) indicates that a password with 0 bits of entropy would only require 1 guess to decode, implying no security as it is completely predictable.

Learn more about Password Entropy here: