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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.

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  • $\begingroup$ Complex zero knowledge proofs like range proofs require dozens of points being transmitted at a time. $\endgroup$ – VincBreaker Dec 26 '18 at 11:49
  • $\begingroup$ They are really used in practice or this is just a research topic? $\endgroup$ – Dima Koshelev Dec 29 '18 at 18:28
  • $\begingroup$ 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. $\endgroup$ – VincBreaker Dec 29 '18 at 20:59

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