How do I calculate the password space of a randomized linked hybrid pasword of 9 images and 10 numbers(0-9)? User allowed to select 4 password

Images=9 Pin= 0-9 Password selection allowed: 4 Every image is linked to a number

Images are randomized at each selection

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Commented Nov 18, 2022 at 7:01
• I am trying to calculate the password space for a graphical password of 9images each image is linked to a number from 0-9.. and users are allowed to select just 4 images Commented Nov 18, 2022 at 7:20
• The answer is 9-choose-4 I think. Commented Nov 18, 2022 at 9:45
• @GloriaJiya So you want to know the keyspace when you have 10 images (images numbered 0 through 9 would total 10 images, not 9) to choose from, and four are picked at random. Is that correct? Commented Nov 18, 2022 at 22:39
• @forest yes that is correct. Commented Nov 19, 2022 at 0:02

The fact that a password is composed of images is irrelevant. If you have 10 possible values for each symbol and choose 4 symbols at random, the keyspace is 104 = 10000, and log2(10000) ≈ 13.3 bits.

This is very insecure!

In general, you can calculate the keyspace by raising the number of possible symbols to the number of randomly-selected symbols. This tells you how many possible combinations there are. You convert this number into the number of bits of security by taking the base-2 logarithm of the result.

For example, if you are choosing a password composed of 12 words chosen at random from a set of 4000, the number of bits of security is log2(400012) ≈ 145 bits, which is secure.

• Ok, for hybrid password password that has a password space for 1st step authentication of 10,000 and 2nd step authentication of 6,000. Do we add 10,000 to 6,000 or multiply 10,000 by 6,000. Commented Nov 20, 2022 at 5:31
• @GloriaJiya Will the attacker know if they got the first password correct before they try the second? Commented Nov 20, 2022 at 22:29
• aforest yes the attacker will know. Commented Nov 21, 2022 at 10:26
• @GloriaJiya In that case, treat it like two separate passwords. First one is broken and then the other, so you aren't adding very much security by using two. Commented Nov 23, 2022 at 22:08
• Okay thank you for the response. Commented Dec 15, 2022 at 8:43