# Composition of ciphertexts in post quantum schemes Kyber and Frodo

I took a look at the Kyber and Frodo procedures and found that the ciphertext consists of two components. In Kyber these are the lines 5-7 in algorithm 2 $$c := (\mathbf{u},v)$$ and in Frodo line 8 of algorithm 10 $$c \leftarrow (C_1,C_2)$$.

One part of the ciphertext pair contains the message to be encrypted, that is $$v$$ in Kyber and $$C_2$$ in Frodo. My question is, therefore, why do you need the other ciphertext component $$\mathbf{u}$$ in Kyber and $$C_1$$ in Frodo? Wouldn't it be sufficient to work with only one, which "hides" the message, that is in Kyber $$v$$ and in Frodo $$C_2$$?

Wouldn't it be sufficient to work with only one, which "hides" the message, that is in Kyber $$v$$ and in Frodo $$C_2$$?
With El Gamal, you have a generator $$g$$ and a public key $$pub$$; to generate a ciphertext for a message $$m$$, you pick a random value $$r$$ and generate the ciphertext $$g^r, pub^r \cdot m$$
So, in El Gamal, the first part of the ciphertext doesn't do anything to "hide" the message, why doesn't we just send the $$pub^r \cdot m$$ part? Well, if we did, the decryptor wouldn't be able to decrypt - after all, he doesn't know what $$r$$ is (and the private key doesn't help him with that), and would be unable to recover $$m$$ from that. By including $$g^r$$, the decryptor (with the private key) is able to recompute $$pub^r$$ and so can remove that from $$pub^r \cdot m$$ to recover $$m$$.