As RFC 4634 describes in section 6.1, SHA-256 is initialized using eight 32-bit words.
These were obtained by taking the first 32 bits of the fractional parts of the square roots of the first eight prime numbers:
H(0)0 = 6a09e667 H(0)1 = bb67ae8 H(0)2 = 3c6ef372 H(0)3 = a54ff53a H(0)4 = 510e527f H(0)5 = 9b05688c H(0)6 = 1f83d9ab H(0)7 = 5be0cd19
These are obviously meant to be "nothing up my sleeves" numbers.
Assuming interoperability — read: compatibility between users — isn't an issue, I've got the following questions:
Are there any security issues related to replacing those SHA-256 initialisation values?
The plan is the one-time use of a CSPRNG to get alternative values for a specific (in-house) implementation; which I presume to be a safe way to get good alternative values. Please correct me when this assumption is wrong.
Are some initialisation values worse than others?
In other words: is the Merkle–Damgård construction, and/or the SHA-2 algorithm design as a whole, susceptible to weak initialisation values along the lines of 0-key problems as applicable to cipher analysis? Or could we set them all to zero without any impact on cryptographic security?
NB: pointers to related research paper(s) welcome, but not a "must".