True or false: "EC encryption — analogous to RSA — is deterministic."

False — EC encryption (ElGamal/VM98) is automatically probabilistic because each encryption uses a fresh random ephemeral exponent $i$. This is a key advantage over schoolbook RSA.

Why EC encryption is probabilistic:

• Each encryption generates a random $i$
• The ephemeral key $K_E = i \cdot P$ and masking key $K_M = i \cdot Q$ change every time
• The same plaintext encrypted twice produces different ciphertexts
• No two encryptions are alike, even for the same message and same public key

Contrast with RSA:

• Schoolbook RSA: $c = m^e \mod N$ — same message → same ciphertext (deterministic)
• RSA needs OAEP padding to become probabilistic
• EC ElGamal is probabilistic by construction — no padding needed

Implications:

• No codebook attacks possible against EC encryption
• No table lookup attacks
• No statistical pattern leakage
• This is one reason EC encryption is considered more elegant than RSA

Important nuance: If the same $i$ is reused (like the Sony PS3 bug for ECDSA), the encryption becomes effectively deterministic and the secret key can be recovered. Fresh randomness for every operation is critical.

Go deeper:

• Probabilistic encryption — Wikipedia — why randomised encryption makes the same plaintext yield different ciphertexts.
• ElGamal encryption — Wikipedia — probabilistic by construction via a fresh ephemeral value.