# RareSkills Authors - Encrypted Polynomial Evaluation (Highlights)  ## Metadata **Review**:: [readwise.io](https://readwise.io/bookreview/38848928) **Source**:: #from/readwise #from/reader **Zettel**:: #zettel/fleeting **Status**:: #x **Authors**:: [[RareSkills Authors]] **Full Title**:: Encrypted Polynomial Evaluation **Category**:: #articles #readwise/articles **Category Icon**:: 📰 **URL**:: [www.rareskills.io](https://www.rareskills.io/post/encrypted-polynomial-evaluation) **Host**:: [[www.rareskills.io]] **Highlighted**:: [[2024-03-20]] **Created**:: [[2024-03-21]] ## Highlights - Instead, the prover computes the encrypted value of x, x², and x³ and gives those the verifier separately. That is, the prover is squaring and cubing on behalf of the verifier. ([View Highlight](https://read.readwise.io/read/01hsds79xjy4n2637aks0mh28w)) ^695396794 - Instead, what we do is have a trusted third party generate a secret τ value and encrypt it ([View Highlight](https://read.readwise.io/read/01hsdsk7ztkxvbzmj1d90ddv3x)) ^695399158 power of taus - And we evaluate it directly on τ, then multiply the result by the generator, we will get the same point. ([View Highlight](https://read.readwise.io/read/01hsdx18nrrgj45ch4bph6776p)) ^695415450  - The Schwartz-Zippel Lemma says that two unequal polynomials almost never overlap except at a number of points constrained by the degree. ([View Highlight](https://read.readwise.io/read/01hsdx3ebm13zwbm47wr3a8h4p)) ^695415534 - Another teaser is that the setup ceremony “powers of tau” derives its name from creating a lot of powers of a hidden value so encrypted polynomials can be calculated from it, similar to what we described in this section. ([View Highlight](https://read.readwise.io/read/01hsdx6d24vhb95kdwxxj013fz)) ^695415718