What is the implication of $VNP = VP$ to cryptography schemes such as Elliptic curve/Abelian Variety/Arithmetic Geometry based cryptography? Are there any papers or books that talk about sophisticated encryption techniques and the possible complexity classes they belong to?
There seems to be a negative implication for RSA if $VNP = VP$. On the other hand no OWF should exist if $VNP = VP$. However relatively nothing is known about frailty of candidate OWF from Arithmetic Geometry if $VNP = VP$. Will these be safe?