It has recently become apparent that both accidental and maliciously caused randomness failures pose a real and serious threat to the security of cryptographic primitives, and in response, researchers have begone the development of primitives that provide robustness against these. In this paper, however, we focus on standardized, widely available primitives. Specifically, we analyze the RSA-OAEP encryption scheme and RSA-PSS signature schemes, specified in PKCS#1, using the related randonmess security notion introduced by Paterson et al. (PKC 2014) and its extension to signature schemes. We show that, under the RSA and (phi)-hiding assumptions, RSA-OAEP encryption is related randomness secure for a large class of related randomness functions in the random oracle model, as long as the recipient is honest, and remains secure even when additionally considering malicious recipients, as long as the related randomness functions does not allow the malicious recipients to efficiently compute the randomness used for the honest recipient. We furthermore show that, under the RSA assumption, the RSA-PSS signature scheme is secure for any class of related randomness functions, although with a non-tight security reduction. However, under additional, albeit somewhat restrictive assumptions on the related randomness functions and the adversary, a tight reduction can be recovered. Our results provides some reassurance regarding the use of RSA-OAEP and RSA-PSS in environments where randonmess failures might be a concern. Lastly, we note that, unlike RSA-OAEP and RSA-PSS, several other schemes, including RSA-KEM, part of ISO 18033-2, and DHIES, part of IEEE P1363a, are not secure under simple repeated randonmess attacks.
