Shamir's Secret Sharing: How to share a secret s to n parties so that a threshold >= t of them can reconstruct the secret.

Choose a random polynomial p of degree t-1 passing through (0,s). Share secrets p(x) to each party 1 <= x <= n.

Any threshold >= t parties can use Lagrange Interpolation to make a polynomial p1 and evaluate p1(0) to recover the secret s.

n.b. this works over finite fields used in cryptography #moonmath

#moonmath manual adventure is over (or begun)

For sure the book deserves another run. But it is really a good introduction and I warmly recommend it to anyone interested in the nitty gritty math details of the topic

Now I just started going through the Maksym Petkus paper
https://arxiv.org/abs/1906.07221

This paper is amazing and IMO contains the best explanation of the foundations I ever read

#moonmath zk-SNARKs challenge 🌑 - Week 4 (and half 😃)

Entering the formal languages shire
✅ Decision functions, Instance & Witness
✅ Statements representations: R1CS, Algebraic Circuits, QAP
✅ Circuit compilers and PAPER toy language

IMO this is easier to digest than the ECC chapters. But may be subjective

Next stop - Groth16 Protocol gran finale

#cryptography #zeroknowledge #zkSNARKs

#moonmath zk-SNARKs challenge 🌑 - Week 3

Exiting elliptic curves rollercoaster
✅ Full torsion groups
✅ Pairings
✅ Construction via complex multiplication method

Math is getting hard 🤯🤯🤯

Next stop statements representation using Rank-1 Quadratic Constraint Systems

#cryptography #zeroknowledge #zkSNARKs

#moonmath zk-SNARKs challenge 🌑 - Week 2

On elliptic curves rollercoaster
✅ Weierstrass form (affine and projective)
✅ Montgomery form
✅ Twisted Edwards form

Discovered some clever tricks to eventually improve my old-good cry library to gain up to 10x speed

#cryptography #zeroknowledge #zkSNARKs

https://tinyurl.com/3ybj4cps

#moonmath zk-SNARKs challenge 🌑 - Week 1

✅ introductory algebra
✅ prime fields extensions
✅ projective planes

So far so good, next stop elliptic curves

#cryptography #zeroknowledge #zkSNARKs

https://tinyurl.com/3ybj4cps

Let the #ZK-SNARKs adventure begin!!! 🤓

Booting up from the #moonmath manual https://github.com/LeastAuthority/moonmath-manual