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RisenCrypto / RisenCrypto.github.io

Write ups on Mathematical Cryptography
https://risencrypto.github.io/
MIT License
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Kate/ #8

Open utterances-bot opened 10 months ago

utterances-bot commented 10 months ago

The KZG/Kate Polynomial Commitment Scheme – Risen Crypto – Mathematical Cryptography, zkSNARKs

https://risencrypto.github.io/Kate/

tarassh commented 10 months ago

Great article,

I have a question, for "Batch Mode Single Polynomial, multiple points" it is not clear how verifier gets commitment to CF. Is it identical to previous chapter, committer sends CF=F(a)⋅G first?

RisenCrypto commented 9 months ago

Great article,

Thank you.

I have a question, for "Batch Mode Single Polynomial, multiple points" it is not clear how verifier gets commitment to CF. Is it identical to previous chapter, committer sends CF=F(a)⋅G first?

Yes, it's the same. In almost all proofs, the Prover sends the Commitment of a polynomial to the Verifier. Occasionally, there are some cases where a Polynomial is an addition of smaller polynomials - in that case if the prover has already sent the commitment of the smaller polynomials to the verifier, then the verifier can compute the commitment of the polynomial himself because KZG commitments are additively homomorphic.