zkSNARK

zkSNARK

• We are using the libsnark library.
• The mtxq balancing equation validation is the match transaction family is replaced with a zkSNARK protocol.

Representing balancing equation as R1CS problem

General form of the equations where i:initiating quantity, n: ratio numerator quantity, d:ratio denominator quantity, r: reciprocating quantity.

i_q * n_q / d_q = r_q for q in {quantity value, quantity unit, quantity resource}

Rewrite as algebraic circuit.

i_q * n_q - d_q * r_q = 0 for q in {0..2}

Rewrite as conjuction of three balancing equation using a slack variable.

i_q * n_q - d_q * r_q + 1 = s_q for q in {0..2} product(s_q) = 1 for q in {0..2}

Rewrite as statements of the form c = a * b

1. in₀ = i₀ * n₀

2. dr₀ = d₀ * r₀

3. indr₀ = in₀ - dr₀

4. s₀ = indr₀ + 1

5. in₁ = i₁ * n₁

6. dr₁ = d₁ * r₁

7. indr₁ = in₁ - dr₁

8. s₁ = indr₁ + 1

9. in₂ = i₂ * n₂

10. dr₂ = d₂ * r₂

11. indr₂ = in₂ - dr₂

12. s₂ = indr₂ + 1

13. ss = s₀ * s₁

14. out = s₂ * ss

Create R1CS as zkSNARK library relation.