Perry E. Metzger wrote: > Actual practical impact on cryptography? Likely zero, even if it turns > out the proof is correct (which of course we don't know yet), but it > still is neat for math geeks.
Right. He constrains his proof to dealing with a specific subset of Dirichlet zeta functions, which means he's not proving GRH or ERH, the former of which would have some - mostly theoretical - implications on crypto in the sense that it would make a number of primality algorithms, previously running in "assumed P", provably polynomial-time. Even if he proved GRH, I don't think the implications for crypto would be particularly great -- yes, things like Miller-Rabin would provably run in O(ln(n)^4), but AKS already runs in provably-polynomial time without dependencies on unproved theorems, and has been improved to comparable speed: O(ln(n)^k) | k=4+epsilon for certain cases, upper bound k=6+epsilon [1], possibly faster since the last time I looked.
Cheers, Ivan.
[1] See Crandall, Papadopoulos: "On the implementation of AKS-class primality tests" (March 2003)
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