[FOM] Provable security and foundations of mathematics

Joe Shipman joeshipman at aol.com
Thu Jun 13 00:26:44 EDT 2019

Except for the common complaints about poor quality of refereeing and proof checking, there were no substantive foundational issues in the Koblitz exchange, which was interesting nonetheless.

But there certainly is important foundational relevance in the question of whether the foundations of mathematics suffice to provide “provable security” for cryptographic systems.  In particular, this depends strongly on the status of P vs NP and related foundational questions. If P=NP, then provable security seems much harder to attain.

— JS

Sent from my iPhone

> On Jun 11, 2019, at 6:24 PM, Timothy Y. Chow <tchow at math.princeton.edu> wrote:
> Jose Manuel Rodriguez Caballero wrote:
>> There are several positions concerning whether the foundations of mathematics are enough in order to develop a branch of cryptography known as provable security. One of the most controversial papers in this debate is the following one:
> That paper was indeed controversial, but the controversy had nothing to do with "whether the foundations of mathematics are enough."  The debate was over sociological issues, such as whether certain people exhibit slipshod scholarship, engage in ad hominem attacks, overstate the significance of their results, misleadingly downplay important limitations and caveats, and so forth.  I don't see any f.o.m. issues of substance at stake here.
> Tim
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