diff --git a/tests/node/tests/lib/BigIntUtils.mjs b/tests/node/tests/lib/BigIntUtils.mjs
index 1a6b7c0f..134b8345 100644
--- a/tests/node/tests/lib/BigIntUtils.mjs
+++ b/tests/node/tests/lib/BigIntUtils.mjs
@@ -1,10 +1,63 @@
 import TestRegister from "../../../lib/TestRegister.mjs";
-import { parseBigInt, egcd } from "../../../../src/core/lib/BigIntUtils.mjs";
+import { parseBigInt, egcd, modPow } from "../../../../src/core/lib/BigIntUtils.mjs";
 import it from "../../assertionHandler.mjs";
 import assert from "assert";
 
 TestRegister.addApiTests([
-    it("BigIntUtils: egcd - basic", () => {
+    // ===== parseBigInt tests =====
+    it("BigIntUtils: parseBigInt - decimal number", () => {
+        const value = parseBigInt("1", "test value");
+        assert.deepStrictEqual(value, BigInt("1"));
+    }),
+
+    it("BigIntUtils: parseBigInt - large decimal", () => {
+        const value = parseBigInt("123456789012345678901234567890", "test value");
+        assert.deepStrictEqual(value, BigInt("123456789012345678901234567890"));
+    }),
+
+    it("BigIntUtils: parseBigInt - hexadecimal lowercase", () => {
+        const value = parseBigInt("0xff", "test value");
+        assert.deepStrictEqual(value, BigInt("255"));
+    }),
+
+    it("BigIntUtils: parseBigInt - hexadecimal uppercase", () => {
+        const value = parseBigInt("0xFF", "test value");
+        assert.deepStrictEqual(value, BigInt("255"));
+    }),
+
+    it("BigIntUtils: parseBigInt - large hexadecimal", () => {
+        const value = parseBigInt("0x123456789ABCDEF", "test value");
+        assert.deepStrictEqual(value, BigInt("0x123456789ABCDEF"));
+    }),
+
+    it("BigIntUtils: parseBigInt - whitespace trimming", () => {
+        const value = parseBigInt("  42  ", "test value");
+        assert.deepStrictEqual(value, BigInt("42"));
+    }),
+
+    it("BigIntUtils: parseBigInt - invalid input (text)", () => {
+        assert.throws(() => parseBigInt("test", "test value"), {
+            name: "Error",
+            message: "test value must be decimal or hex (0x...)"
+        });
+    }),
+
+    it("BigIntUtils: parseBigInt - invalid input (hex without prefix)", () => {
+        assert.throws(() => parseBigInt("FF", "test value"), {
+            name: "Error",
+            message: "test value must be decimal or hex (0x...)"
+        });
+    }),
+
+    it("BigIntUtils: parseBigInt - invalid input (mixed)", () => {
+        assert.throws(() => parseBigInt("12abc", "test value"), {
+            name: "Error",
+            message: "test value must be decimal or hex (0x...)"
+        });
+    }),
+
+    // ===== egcd tests =====
+    it("BigIntUtils: egcd - basic coprime", () => {
         const a = BigInt("36");
         const b = BigInt("48");
         const gcd = BigInt("12");
@@ -13,16 +66,85 @@ TestRegister.addApiTests([
         assert.deepStrictEqual(egcd(a, b), [gcd, bezout1, bezout2]);
     }),
 
-    it("BigIntUtils: parseBigInt - basic", () => {
-        const value = parseBigInt("1", "test value");
-
-        assert.deepStrictEqual(value, BigInt("1"));
+    it("BigIntUtils: egcd - coprime numbers", () => {
+        const [g, x, y] = egcd(BigInt("3"), BigInt("11"));
+        assert.strictEqual(g, BigInt("1"));
+        // Verify Bézout identity: a*x + b*y = gcd
+        assert.strictEqual(BigInt("3") * x + BigInt("11") * y, g);
     }),
 
-    it("BigIntUtils: parseBigInt - not an int", () => {
-        assert.throws(() => parseBigInt("test", "test value"), {
-            name: "Error",
-            message: "test value must be decimal or hex (0x...)"
-        });
+    it("BigIntUtils: egcd - non-coprime numbers", () => {
+        const [g, x, y] = egcd(BigInt("240"), BigInt("46"));
+        assert.strictEqual(g, BigInt("2"));
+        // Verify Bézout identity
+        assert.strictEqual(BigInt("240") * x + BigInt("46") * y, g);
+    }),
+
+    it("BigIntUtils: egcd - with zero", () => {
+        const [g, x, y] = egcd(BigInt("17"), BigInt("0"));
+        assert.strictEqual(g, BigInt("17"));
+        assert.strictEqual(x, BigInt("1"));
+        assert.strictEqual(y, BigInt("0"));
+    }),
+
+    it("BigIntUtils: egcd - identical numbers", () => {
+        const [g, x, y] = egcd(BigInt("42"), BigInt("42"));
+        assert.strictEqual(g, BigInt("42"));
+        // Verify Bézout identity
+        assert.strictEqual(BigInt("42") * x + BigInt("42") * y, g);
+    }),
+
+    it("BigIntUtils: egcd - large numbers", () => {
+        const a = BigInt("123456789012345678901234567890");
+        const b = BigInt("987654321098765432109876543210");
+        const [g, x, y] = egcd(a, b);
+        // Verify Bézout identity
+        assert.strictEqual(a * x + b * y, g);
+    }),
+
+    // ===== modPow tests =====
+    it("BigIntUtils: modPow - basic", () => {
+        // 2^10 mod 1000 = 1024 mod 1000 = 24
+        const result = modPow(BigInt("2"), BigInt("10"), BigInt("1000"));
+        assert.strictEqual(result, BigInt("24"));
+    }),
+
+    it("BigIntUtils: modPow - RSA-like example", () => {
+        // Common RSA public exponent
+        const base = BigInt("123456789");
+        const exp = BigInt("65537");
+        const mod = BigInt("999999999999");
+        const result = modPow(base, exp, mod);
+        // Result should be less than modulus
+        assert(result < mod);
+        assert(result >= BigInt("0"));
+    }),
+
+    it("BigIntUtils: modPow - exponent zero", () => {
+        // Any number^0 = 1
+        const result = modPow(BigInt("999"), BigInt("0"), BigInt("100"));
+        assert.strictEqual(result, BigInt("1"));
+    }),
+
+    it("BigIntUtils: modPow - base zero", () => {
+        // 0^n = 0
+        const result = modPow(BigInt("0"), BigInt("5"), BigInt("100"));
+        assert.strictEqual(result, BigInt("0"));
+    }),
+
+    it("BigIntUtils: modPow - large exponent", () => {
+        // Test with very large exponent (efficient algorithm should handle this)
+        const result = modPow(BigInt("3"), BigInt("1000000"), BigInt("1000000007"));
+        assert(result >= BigInt("0"));
+        assert(result < BigInt("1000000007"));
+    }),
+
+    it("BigIntUtils: modPow - modular inverse verification", () => {
+        // If a*x . 1 (mod m), then modPow(a, 1, m) * x . 1 (mod m)
+        const a = BigInt("3");
+        const m = BigInt("11");
+        const x = BigInt("4"); // inverse of 3 mod 11
+        const result = modPow(a, BigInt("1"), m) * x % m;
+        assert.strictEqual(result, BigInt("1"));
     }),
 ]);