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Is SHA-512 bijective when hashing a single 512-bit block?

Is there any guarantee that there are no collisions for all 512-bit input values for SHA-512 (every 512-bit input has a unique output), or just that they are highly improbable and can't be algorithmically deduced?

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    $\begingroup$ Welcome to Cryptography Stack Exchange. I closed your question as we had a quite similar one (with a good answer) a time ago - the answer is essentially, no, for both parts of your question. $\endgroup$ Jun 5, 2012 at 18:18
  • $\begingroup$ It's highly probable that they exist, they're just hard to find. $\endgroup$ Jun 6, 2012 at 21:46


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