Note on the RKA security of Continuously Non-Malleable Key-Derivation Function from PKC 2015

Qin, Liu, Yuen, Deng, and Chen (PKC 2015) gave a new security notion of key-derivation function (KDF), continuous non-malleability with respect to Φ-related-key attacks (Φ-CNM), and its application to RKA-secure public-key cryptographic primitives. They constructed a KDF from cryptographic primitives and showed that the obtained KDF is Φhoe&iocr-CNM, where Φhoe&iocr contains the identity function, the constant functions, and functions that have high output-entropy (HOE) and input-output collision-resistance (IOCR) simultaneously. This short note disproves the security of their KDF by giving Φhoe&iocr-RKAs by exploiting the components of their KDF. We note that their proof is still correct for Φ-CNM for a subset of Φhoe&iocr; for example the KDF satisfiesΦpoly(d)-CNM, in which an adversary can tamper with a secret by using polynomials of degree at most d.