How can I show, that RSA with OWP is IND-CPA secure by using H function?

How can I show, that RSA with OWP is IND-CPA secure by using H function , a random oracle model.

The Encryption goes like: $$\text{Encryption_H_PK}(M)\gets(C_1,C_2)\gets(f(x),H(x)\oplus M)$$

Decryption goes like: $$M\gets H(x)\oplus C_2$$

• First clarify what's meant by "RSA with OWP" (it's unclear to me: OWP could be an assumed property of RSA); and the relation this (or part of it) has to the question's $f$. Also, figure out how $x$ is obtained in decryption. Then: assume an hypothetical algorithm wining the CPA game, and turn it into one that, with the help of the random oracle, contradicts the hypothesis made on $f$. Conclude by contraposition. – fgrieu Apr 22 '20 at 5:05
• owp means a one way permutation – Skadoosh Apr 22 '20 at 5:09
• also can you suggest why this does not provide chosen cipher text attack security – Skadoosh Apr 22 '20 at 5:10
• Yes, OWP undoubtedly means one way permutation; the unclear thing is with. Is RSA assumed to be a OWP, or is RSA used with some other OWP? – fgrieu Apr 22 '20 at 5:18
• RSA here is assumed to be a OWP – Skadoosh Apr 22 '20 at 5:19