# Is it necessary to transmit two or three points of an elliptic curve?

Are there cryptographic protocols, where a party should transmit by communication channel simultaneously two or three $$\mathbb{F}_q$$-points of an elliptic curve over a finite field $$\mathbb{F}_q$$? Therefore we need a faster compress-decompression method for these two or three points, than just $$x$$-coordinates. The latter requires solving two or three quadratic equations to find $$y$$-coordinates.

I just invented one interesting method such that compression is bit slower, but decompression is much faster. Number of bits in the compressed form remains the same, i.e., $$2\log(q)$$ or $$3\log(q)$$ respectively. Is it useful for cryptographic society? If I am right, the Diffie-Hellman protocol and ECDSA require transmit just one point for each party.

• Complex zero knowledge proofs like range proofs require dozens of points being transmitted at a time. – VincBreaker Dec 26 '18 at 11:49
• They are really used in practice or this is just a research topic? – Dima Koshelev Dec 29 '18 at 18:28
• I know of usages of ZKP in the cryptocurrency field (like in the CryptoNote or Monero's RingCT), I'm sure there are other fields using zero knowledge proofs a lot. – VincBreaker Dec 29 '18 at 20:59