diff --git a/src/functions/shamir_secret_sharing.js b/src/functions/shamir_secret_sharing.js
index def4f16..ed896e3 100644
--- a/src/functions/shamir_secret_sharing.js
+++ b/src/functions/shamir_secret_sharing.js
@@ -54,8 +54,13 @@ module.exports = function (S) {
     };
 
     S.__shamirFn = (x, q) => {
+        // Evaluate the polynomial q[0] + q[1]*x + ... + q[n-1]*x^(n-1) with
+        // Horner's method, using the coefficient position as the exponent.
+        // (indexOf-based evaluation returned the first occurrence of a value,
+        // corrupting the result whenever coefficients repeat.)
         let r = 0;
-        for (let a of q) r = S.__GF256_add(r, S.__GF256_mul(a, S.__GF256_pow(x, q.indexOf(a))));
+        for (let i = q.length - 1; i >= 0; i--)
+            r = S.__GF256_add(S.__GF256_mul(r, x), q[i]);
         return r;
     };
 
@@ -121,19 +126,20 @@ module.exports = function (S) {
         e = S.generateEntropy({hex:false});
         ePointer = 0;
 
-        let w;
         for (let b = 0; b < secret.length; b++) {
             let q = [secret[b]];
 
+            // Sample coefficients uniformly at random from GF(256) (i.i.d.).
+            // No rejection filter: forcing distinct coefficients (and distinct
+            // from the secret byte) violates Shamir's perfect-secrecy
+            // guarantee. Position-based evaluation in __shamirFn handles
+            // repeated values correctly.
             for (let i = 0; i < threshold - 1; i++) {
-                do {
-                    if (ePointer >= e.length) {
-                        ePointer = 0;
-                        e = S.generateEntropy({hex:false});
-                    }
-                    w  = e[ePointer++];
-                } while (q.includes(w));
-                q.push(w);
+                if (ePointer >= e.length) {
+                    ePointer = 0;
+                    e = S.generateEntropy({hex:false});
+                }
+                q.push(e[ePointer++]);
             }
 
             for (let i of sharesIndexes)
diff --git a/test/jsbtc.test.js b/test/jsbtc.test.js
index 99a4ce8..83da18c 100644
--- a/test/jsbtc.test.js
+++ b/test/jsbtc.test.js
@@ -580,6 +580,41 @@ describe(`${(browser) ? 'Browser' : 'Node'} test jsbtc library`, function () {
 
             }
         }).timeout(14000);
+
+        it('Polynomial evaluation is position-based (repeated coefficients)', () => {
+            // Regression for the indexOf bug: __shamirFn must use the
+            // coefficient position as exponent, so repeated coefficient
+            // values are evaluated correctly.
+            const explicitEval = (x, q) => {
+                let r = 0;
+                for (let i = 0; i < q.length; i++)
+                    r = __GF256_add(r, __GF256_mul(q[i], __GF256_pow(x, i)));
+                return r;
+            };
+            // q with a repeated coefficient value
+            const q = [7, 9, 9, 3, 9];
+            for (let x = 1; x < 256; x += 13)
+                equal(__shamirFn(x, q), explicitEval(x, q));
+            // random repeats
+            for (let trial = 0; trial < 50; trial++) {
+                const rq = [];
+                for (let i = 0; i < 6; i++) rq.push(Math.floor(Math.random() * 256));
+                for (let x = 1; x < 256; x += 97)
+                    equal(__shamirFn(x, rq), explicitEval(x, rq));
+            }
+        });
+
+        it('Uniform coefficient sampling: high thresholds round-trip', () => {
+            // The old rejection filter forced distinct coefficients (entropy
+            // leak, breakdown at t >= 30). Coefficients are now sampled
+            // uniformly i.i.d.; verify round-trips up to threshold 100.
+            let secret = Buffer.from("high threshold check 0123456789abcdef", 'utf8');
+            for (let i = 30; i <= 100; i += 5) {
+                let shares = __split_secret(i, i, secret);
+                let r = __restore_secret(shares);
+                equal(r.toString('utf8'), secret.toString('utf8'));
+            }
+        });
     });
 
     describe("Private/Public key functions:", function () {