DeriveInterpolatingValue uses integer division instead of modular inverse

[rdubois-crypto]

DeriveInterpolatingValue uses integer division instead of modular inverse this leads to wrong Lagrange coefficients for most quorums (for instance try 1,3 corum).

The bug is invisible for quorums whose denominator happens to be 1 — which includes {1,2}, the quorum used by the existing tests. It only surfaces on other signer subsets.

Reproduction
tsfrost.deriveInterpolatingValue([1n, 3n], 1n) // → 1n (expected 3·2⁻¹ mod L)
frost.deriveInterpolatingValue([1n, 3n], 3n) // → 0n (expected −1·2⁻¹ mod L)

Suggested fix
Reduce mod the subgroup order at each step and invert with extended Euclid:
tsderiveInterpolatingValue(L: bigint[], x_i: bigint) {
const found = L.find(a => a === x_i)
if (!found) throw new Error('invalid parameters')
let num = 1n
let dom = 1n
for (const x_j of L) {
if (x_j === x_i) continue
num = this.modOrder(num * x_j)
dom = this.modOrder(dom * (x_j - x_i))
}
return this.modOrder(num * this.modInverse(dom))
}

private modInverse(a: bigint): bigint {
const m = this.order
let [r, r1] = [this.modOrder(a), m]
let [x, x1] = [1n, 0n]
while (r1 !== 0n) {
const q = r / r1
;[r, r1] = [r1, r - q * r1]
;[x, x1] = [x1, x - q * x1]
}
if (r !== 1n) throw new Error('not invertible')
return this.modOrder(x)
}

(patch coming soon)