How to secure Elliptic Curve ElGamal encryption against known plaintext attacks? If I have an encoding function  $f(x)$ that maps a message $m$ to a point $P$ on a suitable Elliptic Curve $E$ . If I have the public key $Q$ of my recepient then I can encrypt the message as follows:

Choosing a random number $k &lt; n -1 $ where $n$ is the order of the curve E .

Calculating $C = [k] G $ where $G$ is the generator point of the curve E 

Calculating $R = [k]Q $ where $Q$ is the recipient's public key 

Now the message is encrypted by adding $P$ to $R$ to get 
        $C_e$ $( = R + P)$ which is sent along with $C$ to the recepient.

DECRYPTION:

Now for the recepient to decrypt my message they compute $R = [privatekey] C $ (where $C = [k]G $) and simply subtract $R$ from $C_e$ to get the encoded point $P$ back which is then decoded by an inverse function $f^{-1}(x)$ to recover $m$. 
Now , two problems arise : If the attacker knows the plaintext (suppose if I follow a particular format of data while sending messages ) he could encode his guessed plaintext and subtract it from $C_e$ to recover $ R $ back ! . If I used that same $ R  $ to encrypt further "blocks" of my message then the security of the later parts of my message has been breached! 

I realize that doing  something like a scalar multiplication over and over again for every block of data, would be a huge drawback in efficiency and speed. 

Is there any way to compute a different $ R $ for every block of data, without using much resources and that too quickly ? 

Does reusing the same $R$ for another message break security ?

NOTE: This question is for educational purposes only. It's for the sake of expanding my knowledge on Crypto.
Is there any way to compute a different $R$ for every block of data, without using much resources and that too quickly ?


There's no common way. Standard practice is hybrid encryption per ECIES.

In a nutshell, ECIES is the same as EC-ElGamal with regard to $E$, $G$, $\text{privatekey}$, $Q$, $k$, $C$, $R$, but the shared secret $R$ is used (after a key derivation step) as the key to a symmetric authenticated cipher that conveys the message $m$. This removes the burden of mapping $m$ to a point on the curve, which severely limits the size of $m$, and typically is iterative thus has the potential to leak information about $m$ by side channels.


  Does reusing the same $R$ for another message break security (in EC-ElGamal)?


Yes. Assume $m_0$ and $m_1$ mapped to $P_0$ and $P_1$ are encrypted with the same $R$, into $C_0$ and $C_1$. It holds $C_0=R+P_0$ and $C_1=R+P_1$, therefore $P_1=P_0-C_0+C_1$. Thus $m_1$ can be found from $m_0$ and ciphertext. With $R$ fixed, the cipher is insecure under known-plaintext attack.

Additions per comment:


Even if the attacker has no knowledge of a plaintext $m_0$, s/he does learn something about the plaintext. In particular she can tell if $m_0=m_1$, since that's equivalent to $C_0=C_1$. This qualifies as a break, since the objective of encryption is to prevent adversaries from learning anything about plaintext (except its length). As an example, this allows to distinguish between a routine Have a quiet nightshift Joe ($m_0=m_1$) from an exceptional Launch missile to target A ($m_0\ne m_1$).
Doubling $R$ at each message would be extremely insecure. It would hold $P_j+P_j-P_{j+1}=C_j+C_j-C_{j+1}$, and that allows to decipher any message sent encrypted twice, as $P_j=P_{j+1}=C_j+C_j-C_{j+1}$.