# CPA attack against Symbol obusfcation

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 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?

• 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? – kelalaka Mar 15 at 8:07
• @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? – Riva11 Mar 15 at 15:38
• 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. – kelalaka Mar 15 at 15:51
• 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? – Riva11 Mar 15 at 19:30
• 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. – kelalaka Mar 15 at 19:36