Bruce Schneier has long written that the probability is unacceptably high that the NSA has installed a PRNG backdoor in the widely accepted SHA-3 standard protocol for cryptography (which NIST grudgingly accepted only with a footnoted caveat that one might prefer to use a more efficient alternative).
Not true. NIST (not the NSA!) suggested to merely increase the capacity of the SHA3 sponge construction. This only increases entropy and security. Bruce Schneier criticized this not because this would possible imply any backdoor, but simply because NIST changing parameters at all might reduce general acceptance.And you have obviously no idea how SHA3 works. There is no (P)RNG in SHA3 whatsoever.
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If such a backdoor exists (which seems nearly certain to me), the NSA can rather easily crack into any level it chooses of such encryption, and that means virtually all the BTC protocols - which would be the rather instant death of such cryptocurrencies. Is Quarkcoin the only alternative cryptocoin that does not use the tainted PNRG? 
1. SHA3 has absolutely nothing to do with Bitcoin.2. SHA3 has nothing to do with encryption, it's is a hashing function. That's something completely different. It's both part of a technology field we call 'cryptography', but encryption ≠ hashing.