Here's a structured breakdown of potential flaws, concerns, and improvements in the code.

[coryscotthodson-png]

⚠️ Issues and Fixes

1. Incorrect Power Indexing in __shamirFn

Problem:

for (let a of q) r = S.__GF256_add(r, S.__GF256_mul(a, S.__GF256_pow(x, q.indexOf(a))));

q.indexOf(a) is not safe in case of duplicate values — it returns the first index.

Polynomial evaluation should use actual index position, not indexOf.

✅ Fix:

for (let i = 0; i < q.length; i++) {
r = S.__GF256_add(r, S.__GF256_mul(q[i], S.__GF256_pow(x, i)));
}

---

2. Broken Lagrange Interpolation Denominator

Problem in __shamirInterpolation:

let a = points[m][0];
let b = S.__GF256_add(points[j][0], points[m][0]); // <-- incorrect
let c = S.__GF256_div(a, b);

This deviates from the standard Lagrange interpolation, where:

L_j(x) = \prod_{m \ne j} \frac{x - x_m}{x_j - x_m}

✅ Fix:

let numerator = S.__GF256_sub(0, points[m][0]); // x = 0 for secret recovery
let denominator = S.__GF256_sub(points[j][0], points[m][0]);
let fraction = S.__GF256_div(numerator, denominator);
p_j_x = S.__GF256_mul(p_j_x, fraction);

---

3. Random Coefficients May Include Duplicates

Problem:

do {
w = e[ePointer++];
} while (q.includes(w));

You're rejecting duplicate coefficients unnecessarily. Shamir's scheme allows duplicate y-values, and it's unlikely to matter for securely chosen randomness.

This can also reduce entropy or cause rejection loops.

✅ Optional Fix:

Remove this rejection unless you have a specific reason to avoid duplicates in coefficients.

---

4. Ambiguous Bit Mask in Share Indexing

Problem:

let index_mask = 2 ** indexBits - 1;

You're using indexBits=8 by default, which is fine, but if someone uses fewer bits, the randomness space shrinks.

Might be okay depending on use-case, but it's worth noting for security guarantees.

---

✅ Summary Fixes (Required)

Fix Description

✅ __shamirFn Use loop index, not indexOf()
✅ __shamirInterpolation Use sub, not add, for Lagrange denominator
⚠️ Random coeffs Consider allowing duplicates unless provable issue
⚠️ Share index mask Ensure entropy remains secure if bits reduced

Input:

threshold: minimum number of shares needed to reconstruct.

total: total number of shares to generate.

secret: the secret split byte-by-byte.

indexBits: how many bits to use for the x-coordinate (defaults to 8).

It generates total number of shares with unique non-zero x-coordinates.

For each byte of the secret:

Constructs a random polynomial of degree threshold - 1, with secret byte as the constant term.

Evaluates this polynomial at all chosen x-values to produce shares.

---

⚠️ Critical / Possible Bugs or Concerns

1. Invalid index selection due to indexBits logic

let index_mask = 2**indexBits - 1;
if (total > index_mask) throw new Error("index bits is to low");

Should be:

if (total > index_mask + 1) throw new Error("index bits too low");

Reason: index_mask is the maximum value, and you skip index 0, so the number of usable indexes is only index_mask.

Fix suggestion:

if (total > index_mask) throw new Error("index bits too low (max usable: " + index_mask + ")");

---

2. index !== 0 check: Why is index 0 skipped?

if ((shares[index] === undefined)&&(index !== 0)) {

Skipping index === 0 may break polynomial interpolation if 0 is a valid input (which it usually is). In classic Shamir's Secret Sharing, x = 0 is often used as the secret.

If you're avoiding x=0 deliberately (e.g., to avoid exposing the secret directly), document this explicitly.

However, this introduces bias and reduces the available index pool.

✅ Skipping x=0 is valid if and only if your Shamir reconstruction algorithm accounts for that and expects only x > 0.

---

3. q.includes(w) check reduces entropy

do {
...
} while (q.includes(w));

This ensures coefficients are unique, but in standard SSS, polynomial coefficients do not need to be unique.

You're reducing entropy unnecessarily by rejecting duplicates.

Fix suggestion: Remove the q.includes(w) check for more entropy and better randomness.

---

4. Ambiguous / unclear functions:

You use:

BF([])

BC([...])

S.__shamirFn(i, q)

These are likely:

BF = byte field / finite field byte conversion

BC = byte concatenation?

S.__shamirFn(x, coeffs) = evaluate polynomial

If these are not secure finite field arithmetic functions over GF(256), then your SSS implementation may break or become insecure.

Ensure: All arithmetic is done in the correct finite field (GF(256)), not modulo 256 unless using proper irreducible polynomial.

---

5. Re-using entropy multiple times

You're generating entropy once and consuming it gradually:

e = S.generateEntropy({hex:false});
...
if (ePointer >= e.length) {
e = S.generateEntropy({hex:false});
ePointer = 0;
}

This is fine if S.generateEntropy gives truly random, cryptographically secure bytes. Just be aware of overusing small entropy pools.

✅ Use a cryptographically secure RNG and re-seed adequately.

---

6. Returned structure is unclear

You return:

return shares;

But shares is an object where each key is the x-coordinate, and value is... a buffer?

This makes sense, but you may want to return it as:

return sharesIndexes.map(i => ({ x: i, y: shares[i] }));

For better serialization and reconstruction clarity.

---

🧠 Suggested Improvements

Add type validation for inputs.

Consider not skipping index 0 (or explicitly document why you are).

Don't enforce uniqueness of polynomial coefficients.

Clarify or rename BF and BC functions.

Return shares as { x, y } tuples, not an object map.

Add test vectors (e.g., compare with known SSS implementations).

---

✅ Example of improvement

if (threshold > 255 || total > 255)
throw new Error("threshold and total must be <= 255");
if (threshold > total)
throw new Error("threshold cannot exceed total");
const index_mask = 2 ** indexBits - 1;
if (total > index_mask)
throw new Error("indexBits too low to generate unique indices");

const shares = {};
const shareIndices = [];
let entropy = S.generateEntropy({ hex: false });
let ePointer = 0;

while (shareIndices.length < total) {
if (ePointer >= entropy.length) {
entropy = S.generateEntropy({ hex: false });
ePointer = 0;
}
const index = entropy[ePointer++] & index_mask;
if (index !== 0 && !(index in shares)) {
shares[index] = BF([]);
shareIndices.push(index);
}
}

entropy = S.generateEntropy({ hex: false });
ePointer = 0;

for (let b = 0; b < secret.length; b++) {
const coeffs = [secret[b]];
for (let j = 1; j < threshold; j++) {
if (ePointer >= entropy.length) {
entropy = S.generateEntropy({ hex: false });
ePointer = 0;
}
coeffs.push(entropy[ePointer++]); // allow duplicates
}
for (const i of shareIndices) {
const y = S.__shamirFn(i, coeffs);
shares[i] = BC([shares[i], BF([y])]);
}
}

return shareIndices.map(i => ({ x: i, y: shares[i] }));

---

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