For the symetric keys it is recommend that the same key should not be used to encrypt large number(2^32) of cipher blocks to avoid the key-exhaustion risk.
Curious to know whether the asymmetric key cryptosystems also has such a risk? i tried to search on internet couldnt find about it
Such a restriction would no make sense in asymmetric encryption schemes where there is a public key value made freely available to all, including the adversary. This gives the adversary the power to create arbitrarily many matched plain and cipher pairs without any restriction. In symmetric (secret key) cryptography, the adversary notionally obtains information from other parties legitimate use of the private key.
Asymmetric encryption can claim legitimate defence against key exhaustion by typically having a much larger ciphertext space combined with non-deterministic variations.
This problem is closely related to tightly-secure encryption schemes in the asymmetric encryption areas (or more precisely in multi-challenge security).
This is because classical security notions like IND-CPA or IND-CCA only consider single-challenge ciphertext. There is a generic transformation from single-challenge to multi-challenge but with a security loss linear to the number of challenge ciphertexts.
Therefore, in theory for asymmetric cryptography, you should not use the same public key too often as well. However, there is a line of research to build tightly-secure encryption schemes, with those schemes you don't need to worry about the "Key Exhaustion Risks".
