If indeed the NSA has made some unknown to the public breakthrough's in math (very likely if you believe the snowden leaks), wouldn't it be a good idea to use at least
two different algorithm's for signatures and hashing (one on top of the other with two different keys).
for example using two public keys, one with RSA and another with ECC over some curve.
if RSA keys are too big then two ECC keys, one with secp256k1 and another with the russian standard for ECC (
https://tools.ietf.org/html/rfc5832).
the NSA most likely won't have a backdoor for the russian curve, the russians won't have a backdoor for the NSA curve.
thats assuming the NSA didn't break ECC completely and can only decrypt backdoored curves.
