I'm trying to contrast key rotation requirements for asymmetric and symmetric ciphers.
In the case of symmetric ciphers, we have the results such as the so called "CBC Theorem" (stated on pg. 24 of https://crypto.stanford.edu/~dabo/cs255/lectures/PRP-PRF.pdf) The CBC Theorem states that for a "q - query" CPA attacker attempting to break semantic security of AES-128-CBC, the attacker's advantage is less than $1/2^{32}$ only if $q^{2}L^{2} / \left\lVert X \right\rVert$, the "error" term in the CBC theorem, is less than $1/2^{32}$, i.e. given that $\left\lVert X \right\rVert = 2^{128}$ for AES-128, we can encrypt $2^{48}$ AES-128 blocks after which we need to switch the key in order to keep the attacker’s advantage below $1/2^{32}$
I have not seen a proof of theorem, but I'm guessing such results arise from basing the security of block cipher modes purely on their behavior as pseudo random functions.
Probabilistic asymmetric encryption schemes such as RSAES-OAEP, ECIES etc., on the other hand, employ the assumption of pseudo randomness in addition to an assumption around (computational) hardness of some number theoretic or algebraic problem, such as hardness of EC/DLP, factoring or short vector problems etc.
Does the fact that asymmetric schemes are based on such dual assumptions (pseudo randomness + factoring etc.) mitigate or extend the horizon for key rotation in such schemes after a certain number of encryptions under the same key, beyond what is implied by relying purely on pseudorandomness as is the case for AES-128-CBC under the CBC theorem? Is there an asymmetric analog for the CBC theorem that quantifies the advantage conferred to an adversary after some number of encryptions under the same key?