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: $M\gets H(x)\oplus C_2$

  • $\begingroup$ 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. $\endgroup$ – fgrieu Apr 22 '20 at 5:05
  • $\begingroup$ owp means a one way permutation $\endgroup$ – Skadoosh Apr 22 '20 at 5:09
  • $\begingroup$ also can you suggest why this does not provide chosen cipher text attack security $\endgroup$ – Skadoosh Apr 22 '20 at 5:10
  • $\begingroup$ 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? $\endgroup$ – fgrieu Apr 22 '20 at 5:18
  • 1
    $\begingroup$ RSA here is assumed to be a OWP $\endgroup$ – Skadoosh Apr 22 '20 at 5:19

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