is SHA-512 collision resistant?

cryptography collision sha sha512
Soumyajit Bhattacharyay picture Soumyajit Bhattacharyay · Mar 12, 2016 · Viewed 8.4k times · Source

According to the books that i have read, it says that S.H.A(Secure Hash Algorithm) is collision resistant.But if the input space is a 1024 bit number and the output space is a 512 bit message digest then shouldn't it be colliding for (2^1024)/(2^512) times? As the range is lesser than the domain being mapped there should have been collisions. please explain where i am going wrong.

Answer

zaph picture zaph · Mar 12, 2016

The chance for a collision does not depend on the input size. The chance to a 512-bit hash collision is 1.4×10^77, see Probability table

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