What is the maximum number of SHA-1 hashes?

Question

Clearly, since SHA-1 hashing generates 40 characters each time there is a finite number of possible hashes, does anyone know exactly how many?

Answer 1

SHA-1 hashes have 160 bits, so 2 ¹⁶⁰ of them.
(2 ¹⁶⁰ = 1461501637330902918203684832716283019655932542976 ~ = 1.46 x 10 ⁴⁸ )

Note that since you have much more message space than possible hashes, collisions will inevitably occur.

Also note that the chance of a collision is much higher than you think. With reports of only 2 ^{80, the} probability of collision is 50%, due to paradox . (i.e. a total of 23 people, the probability that 2 people have the same birthday is 50%).

Answer 2

SHA-1 produces 160-bit outputs, and it should be able to create almost any sequence of 160 bits. There are such ^2,160 such sequences, that is, close to 1461 billion billion billion billion. So big.

However, we have no evidence that each of them is available. It would be bad for SHA-1 security if the number of possible outputs were significantly lower than 2 ¹⁶⁰ ; for example, if only 1/4 of them are achievable (2 ¹⁵⁸ ), then the security against attacks on the proprieto will be divided by 4, and the security against collisions will be reduced by half. This issue is currently not known with SHA-1 (SHA-1's weaknesses are known when it comes to collision resistance, but not that).

It is possible (but it would be at least slightly surprising) that several 160-bit outputs cannot be achieved. It is expected that this will remain unknowable. To some extent, having the opportunity to prove that the possible SHA-1 outputs span the entire 160-bit space, it would be dangerous: such a proof would require a lot of analysis of the mathematical structure of SHA-1, and the security of SHA-1 to a large extent depends on such an analysis is unsolvable.

Answer 3

SHA-1 consists of 5 32-bit integers.

This is 4294967296 ^ 5 or 2 ^ 160

or 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976

To introduce this in perspective

Total Possible SHA-1 values: 1 461 501 637 330 302 918 203 684 832 716 283 019 655 932 542 976 Total amount of water on Earth: 365 904 000 000 000 000 000

This includes every ocean, sea, lake, etc. -

The possibility of a collision is theoretical only at this stage. Still waiting to hear about it.