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We have a transmission system such that a message $m\in[0,1]$ is converted to $N$ symbols $S=[s_1,s_2...s_N]$ and $s_i\in[1,2,3,4]$. The obfuscation of the symbols is as follows:

  1. A key $K1$ seeded to random number generator such that the output of RNG $G=[g_1,g_2,...,g_N]$.
  2. The encrypted symbol $X=[x_1,x_2...x_N]$ and $x_i=(s_i+g_i) \, \mathrm{mod} \, 4, i\in{1,2,...,N}$

How to show the cryptanalysis in terms of the CPA or KPA attacks?

And when second key $K2$ is used to induce a symbol noise $E=[e_1,e_2..,e_N]$ to further increase the complexity of the cipher detection at the attacker as follows:

  • the final encrypted plaintext $C=[c_1,c_2...,c_N]$ such that $c_i=x_i+e_i$ where $0<e_i\leq 1$ knowing that the receiver's detector first round the symbol value to nearest integer.

In this case, are there improvements to reduce the probability of the CPA\KPA attacks?

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    $\begingroup$ Symbol obusfcation is not part of the security that may confuse you. The RNG must be running the same values when the key is feed, so can you see now? $\endgroup$ – kelalaka Mar 15 at 8:07
  • $\begingroup$ @kelakaka it's not clear what you are trying to say. I know the legitimate users need to have the same key. The security relies on the RNG only? $\endgroup$ – Riva11 Mar 15 at 15:38
  • $\begingroup$ Are trying to play the Ind-CPA game? I don't see an IV/nonce here. Doesn't encryption a message again has the same cipher text. $\endgroup$ – kelalaka Mar 15 at 15:51
  • $\begingroup$ Yes i mean the CPA adversary and challenger game. Now the nonce or the input to RNG is actually another question as how often need to be updated? $\endgroup$ – Riva11 Mar 15 at 19:30
  • $\begingroup$ If there is no nonce and the key is always set to initial then can it be KPA secure? Not that you can have at most Ind-CPA secure, since Ind-CCA cannot be achieved without integrity. $\endgroup$ – kelalaka Mar 15 at 19:36

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