# Message Expansion / Encryption Blowup Factor / Ciphertext Expansion of ECC

In order to complete the following table with asymptotic times and message expansions,

$\quad \quad \quad \quad \quad \quad \quad \quad \quad$ RSA $\quad$ McEliece $\quad$ ECC

Encryption Speed $\quad \quad \; \; N^2 \quad \quad N^2 \quad \quad \quad N^3$

Decryption Speed $\quad \quad \; \; N^3 \quad \quad N^2 \quad \quad \quad N^3$

Public Key Size $\quad \quad \quad \;\; N \quad \quad \; \ N^2 \quad \quad \quad N$

Private Key Size $\quad \quad \quad \;\; N \quad \quad \; \ N^2 \quad \quad \quad N$

Message Expansion $\quad \; 1-1 \quad \; 2-1 \quad \quad \quad ?$

I need to find the message expansion of ECC cryptosystem, but I don't find a clear answer anywhere.

Can someone give me and explain the missing value in the table?

• which ECC based public key encryption scheme are you considering here? – SEJPM Jul 28 '16 at 13:45
• Diffie-Hellman and El-Gamal – Leafar Jul 28 '16 at 13:52
• I would say that the answer is 2-1, is it right? – Leafar Jul 28 '16 at 13:58
• DH is not an encryption algorithm and ElGamal has 2, except for when you do hybrid encryption with ElGamal like in ECIES, where you'd get $\infty$-1, depending on your message length. – SEJPM Jul 28 '16 at 14:04
• I was thinking about the common El-Gamal based on the discrete logarithm problem – Leafar Jul 28 '16 at 14:07