Afterthought After writing up this spec, I would also like to question/justify the idea as to whether we need this. My concerns are around file access for things like state management and if there are any cases where a user may, due to ignorance allow one to execute arbitrary code in a non-sandboxed way Problem statement Introduction Noir is a domain specific language for writing circuits. Non-deterministic behaviour is useful as they allow you to prove statements in a more efficient way. For example, when doing an inverse, one can either deterministically use a inversion algorithm, or non-deterministically supply the inverse and verify that it is the inverse, since we know that the inverse of a number multiplied by that number equals 1, except 0. The same applies for other operations like square root. Another form of non-determinism is state fetching.
12/16/2022Introduction In this document, we describe the API that the cryptography layer needs to expose to the verkle trie layer. If you are creating a verkle trie implementation without the cryptography fully being implemented, you can mock the following APIs. Elliptic Curve API We define a Elliptic curve $E$ over a base field $F_p$ with a scalar field $F_r$. The group exposed by $E(F_p)$ must have prime order. This is so that the verkle trie logic does not need to worry about subgroup attack vectors. The group exposes two algorithm:
6/20/2022The formulas were derived by reading the following academic article here
6/20/2022We may use these two terms interchangeably however they are not the same, a vector commitment scheme is strictly more powerful than a polynomial commitment scheme. One can take the dot product between two vectors and if one vector is of the form <1, t, t^2, t^3,..., t^n> then one can realise the dot product as the evaluation of a polynomial in monomial basis at the point t.
6/20/2022or
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